Answers
f(x)=secxcscx
let secx=g(x)
let cscx=h(x)
therefore, using leibnitz rule,
f'(x)=g'(x)*h(x)+h'(x)*g(x)
Since derivative of secx=secxtanx
and derivative of cscx=-cscxcotx,
f'(x)=secxtanxcscx -cscxcotxsecx
=1/cosx*sinx/cosx*1/sinx - 1/sinx*cosx/sinx*1/cosx
=1/cos^2x-1/sin^2x
=(sin^2x-cos^2x)/sin^2xcos^2x / Option1
The value of f'(x) is (sin^2x - cos^2x)/sin^2x cos^2x. Thus, option A is correct.
What are trigonometric identities?Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.
Given;
f(x) = secx cscx
let secx = g(x)
let cscx = h(x)
Using Leibnitz rule,
f'(x) = g'(x)h(x) + h'(x)g(x)
Since the derivative of secx = secx tanx
derivative of cscx = -cscx cotx,
f'(x) = secx tanx cscx - cscx cotx secx
f'(x) = 1/cosx sinx/cosx 1/sinx - 1/sinx cosx/sinx 1/cosx
f'(x) =1/cos^2x - 1/sin^2x
f'(x) = (sin^2x - cos^2x)/sin^2x cos^2x
Thus, option A is correct.
Learn more about trigonometric;
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Related Questions
A group of 9 people are ordering pizza. Each person wants 3 slices and each pizza has 8 slices. How many pizzas should they order?
Answers
Answer:
its 4 pizzas
Step-by-step explanation:
The number of pizzas will be a whole quantity. Then the number of pizzas ordered will be 4.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
A group of 9 people are ordering pizza. Each person wants 3 slices and each pizza has 8 slices.
The total number of slices will be given as,
⇒ 9 x 3
⇒ 27
Then the number of pizzas will be given as,
⇒ 27 / 8
⇒ 3.375
The number of pizzas will be a whole quantity. Then the number of pizzas ordered will be 4.
More about the Algebra link is given below.
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y +4 = 2/3(x – 3)
Write equation in standard form.
Please put a step by step explanation!
Answers
Answer:
2x - 3y = 18Step-by-step explanation:
The standard form is:
ax + by = cGiven equation in point- slope form:
y + 4 = 2/3(x - 3)Convert:
y + 4 = 2/3(x - 3)3y + 12 = 2x - 6-2x + 3y = - 6 - 12-2x + 3y = - 182x - 3y = 181.) the length of a rectangular Garden is double of its breadth.if the area of Garden is 128m2.find the length and breadth
Answers
Area = Length X width
Let the width (breadth) = X
The length is double so it is 2x
Area = X * 2x = 2x^2
128 = 2x^2
Divide both sides by 2:
64 = x^2
take the square root of both sides:
x = 8
The breadth = 8 meters
The length = 16 meters
Write the equation of a circle with radius 10 and center (-7,9) in standard form.
Answers
(x+7)^2 + (y-9)^2=100
(Correct answer get's brainliest)
What is the domain and range of the function?
Match the domain and range with the corresponding set of points.
Answers
Range (-inf, 1)
Range : (-infinity, infinity)
You spent ¼ of your money on lunch.After lunch you gave half of what you had left to the friend,then you spent $3 on a boon. You have $4¼ left. How much money did you have before lunch.
Please explain this. with answer
Answers
Answer:
[tex]total \: you \: have \: = x \\after\: lunch \: you \: have \: = \frac{3x}{4} \\ a fter \: giving \: to \: friend = \frac{3x}{8} \\ after \: spending \: for \: boon = \frac{3x}{8} - 3 = 4 \frac{1}{4} \\ \frac{3x - 8 \times 3}{8} = \frac{17}{4} \\ \frac{3x - 24}{2} = 17 \\ 3x - 24 = 17 \times 2 \\ 3x - 24 = 34 \\ 3x = 34 + 24 \\ 3x = 58 \\ x = \frac{58}{3} \\ x = 19.33 \\ thank \: you[/tex]
Solve: 70 x 103^3.
A 7,000
B 700,000
C 700
D 70,000
Answers
Answer:
D 70,000
Step-by-step explanation:
Answer:
D.
Step-by-step explanation:
simple if you know how to multiply cuz thats all you doing anyway.
anyways you Welcome.
The ages of Sara and Samia are in the ratio 3: 5. Six years from now the ratio of
their ages will be 2:3.Find their present ages. with explanation please
Answers
Answer:
Sara=18 years
Samia=30 years
Step-by-step explanation:
For age questions, the difference of their ages remains the same.
Now 6 years from now
Sara:Samia Difference Sara:Samia Difference
3 : 5 2 2 : 3 1
x2 x2 x2 (times two to make them equal)
4 : 6 2
4-3=1
1 unit=6
Sara=6x3=18
Samia=6x5=30
Hope this helps! Thanks.
When you toss a die while playing a game, you can get 1, 2, 3, 4, 5, or 6 on the top face. How many possible combinations of the top faces for the dice are there if:
a) you must toss 4 dice
b) you must toss n dice
Answers
Using the fundamental counting theorem, it is found that:
a) 1296 combinations are possible.
b) [tex]6^n[/tex] combinations are possible.
The fundamental counting theorem states that for n independents trials, each with [tex]n_1, n_2, n_n[/tex] ways of being done, the total number of combinations is:
[tex]T = n_1 \times n_2 \times ... \times n_n[/tex]
Item a:
Four independent dice throws, each with six outcomes, thus:
[tex]T = 6 \times 6 \times 6 \times 6 = 6^4 = 1296[/tex]
Item b:
n independent dice throws, each with six outcomes, thus:
[tex]T = 6^n[/tex]
A similar problem is given at https://brainly.com/question/24067651
If a circle has a circumference of 40.82cm what would the diameter be show working out
Answers
Answer:
d = 12.99cm
Step-by-step explanation:
The formula of the circumference of a circle is as follows:
[tex]C = \pi d[/tex]
[tex]40.82 = \pi d\\\frac{40.82}{\pi } = d\\ d = 12.99 cm[/tex]
(Show work)
Please help me
Answers
Answer:
8km to miles
8÷1.609
4.97097
Answer:
4.97 miles or approximately 5 miles
Step-by-step explanation:
To get kilometers to miles, you divide by 1.609
So [tex]\frac{8 km}{1.609 mi}[/tex]=4.97 or approximately 5 miles.
How are the two angles related?
Answers
The angles 60 degrees and 120 degrees are related by supplementary.
Supplementary angles:Supplementary angles are angles that sum up to 180 degrees.
In other word, supplementary angles are two angles whose measures add up to 180° .
Therefore, the two angles 60 degrees and 120 degrees are related by supplementary angle. Mathematically
60° + 120° = 180°learn more on angles here:https://brainly.com/question/3027144
Michelle is planting flowers in her garden. She wants the ratio of daisies to carnations to be 3 to 2. Michelle wants to plant a total of 40 flowers. How many daisies should she plant?
A.
21 daisies
B.
8 daisies
C.
24 daisies
D.
38 daisies
Answers
Answer:
C.
24 daisies
Step-by-step explanation:
40 divided by 5 = 8
8 times 3 = 24
8 times 2 = 16
There are 24 daisies and 16 carnations. So the answer is C, 24 daisies.
Please mark brainliest if possible and have a nice day!
(15x7 - 10x3 + 5x2) ÷ (5x2)
Answers
[tex](15x7 - 10x3 + 5x2) \div (5x2) \\ = (15x \times 7 - 10x \times 3 + 5x \times 2) \div (5x \times 2) \\ = (105x - 30x + 10x) \div (10x) \\ = 85x \div (10x) \\ = \frac{85x}{10x} \\ = \frac{17}{2} [/tex]
Solved ✔︎Give me 5 stars plzzzz
In a G.P the 3rd term is 4 times the 1st term and the sum of the 2nd term and the 4th term is 30.find the common ratio,find the sum of the first 7 terms
Answers
Answer:
the common ratio is either 2 or -2.
the sum of the first 7 terms is then either 765 or 255
Step-by-step explanation:
a geometric sequence or series of progression (these are the most common names for the same thing) means that every new term of the sequence is created by multiplying the previous term by a constant factor which is called the common ratio.
so,
a1
a2 = a1×f
a3 = a2×f = a1×f²
a4 = a3×f = a1×f³
the problem description here tells us
a3 = 4×a1
and from above we know a3 = a1×f².
so, f² = 4
and therefore the common ratio = f = 2 or -2 (we need to keep that in mind).
again, the problem description tells us
a2 + a4 = 30
a1×f + a1×f³ = 30
for f = 2
a1×2 + a1×2³ = 30
2a1 + 8a1 = 30
10a1 = 30
a1 = 3
for f = -2
a1×-2 + a1×(-2)³ = 30
-10a1 = 30
a1 = -3
the sum of the first n terms of a geometric sequence is
sn = a1×(1 - f^(n+1))/(1-f) for f <>1
so, for f = 2
s7 = 3×(1 - 2⁸)/(1-2) = 3×-255/-1 = 3×255 = 765
for f = -2
s7 = -3×(1 - (-2)⁸)/(1 - -2) = -3×(1-256)/3 = -3×-255/3 =
= -1×-255 = 255
Please help me solve these 3 questions
Answers
1. To solve algebra equations using the distributive property, we need to distribute (or multiply) the number with each term in the expression. In that way, the brackets are removed. We can then combine like terms and solve by equations when necessary.
2. The first step is simply to apply the distribution using the distributive property : 3(3x-5x)+2=-8 applying the distributive operation we get 9x -15x or we could have simply done 3(2x)+2=-8 which gives us 6x+2=-8 and finally 6x= -8/2= -4
6x=-4 means x= -4/6 thus x= -2/3
3. Multiplication has priority over addition or subtraction thus we have first to apply the distributivity before combining the variable terms
4/5×3/8= the aswer and thanks
Answers
Step-by-step explanation:
[tex] \frac{4}{5} \times \frac{3}{8} [/tex]
Reduce the numbers with the greatest common factor 4
[tex] \frac{1}{5} \times \frac{3}{2} [/tex]
Just multiply, To multiply the fractions , multiply the numerators and denominators separately
[tex] \frac{1 \times 3}{5 \times 2} [/tex]
[tex] \frac{3}{10} [/tex]
That's the answer 3/10 or 0.3
What’s the answer? Please help thank you
Answers
Answer:
-5000
Step-by-step explanation:
hope this helps :)
All angles in the figure at the right are right angles what is the agree of the figure
F.14
G.18
H.28
I.36
Answers
Answer:
Ans: 36
Step-by-step explanation:
just separate it into three rectangles and use the formula
A=l*b
and at last add all of them
find the diameter of the circles having areas of 2464 cm square .
Answers
Answer:
the diameter of a circle is 56 CM
PLSSSSS HELPPP P PP P P P WUICKKKKLYLLYLYLYLYYYYY PLSSSSS
Tammy made $177 for 9 hours of work.
At the same rate, how many hours would she have to work to make $133?
THIS SHOULD BE EASY!!!!!
Answers
Answer:
7 hours
Step-by-step explanation:
If you divide
171 ÷ 9
you find the $ Tammy made in 1 hour.
171 ÷ 9 = 19
So Tammy made 19 for 1 hour of work.
Then we divide 133 by 19 to find out for how many hours she has to work.
133 ÷ 19.67 = 7. So Tammy has to work 7 hours to make $133.
Compact discs are on sale for $13.00 including tax. How many can you buy with $84.00?
Answers
Answer:
You can buy 6
Step-by-step explanation:
You divide 84 by 13 and it will give u a decimal
x−2y=−1
y=5x−3
Choose the correct answer below.
A.
The two lines are perpendicular.
B.
The two lines are neither parallel nor perpendicular.
C.
The two lines are parallel.
D.
More information is needed.
Answers
b.
they're just intersecting.
Explain a set of parallel lines and a transversal line within this image.
Plz help me, thx you so much
Answers
The table gives the temperature (in) in five cities at 6 am on the same day. Use the table to answer the questions
Answers
Answer:
a) 32
b) 6
Step-by-step explanation:
which graph shows proportional relationship between x and y
Answers
6.1 times 10 to the 4th power
Answers
Answer:
61,000
Step-by-step explanation:
[tex]6.1[/tex]·[tex]10^{4}[/tex]
6.1·10000
61,000
Answer:
61,000
Step-by-step explanation:
6.1 · 10^4
6.1 · 10,000=
61,000
Will mark brainliest to best answer, i need it asap!!!!!!!!!!!!!
Answers
[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
The Above statement can be represented as :
[tex] \dfrac{a - 15}{10} [/tex]so, the correct choice is A.
Simplify the following algebraic expression by combining like terms 2x - 2 + x + 4
Answers
Answer:
3x+2
Step-by-step explanation:
2x-2+X+4
= 2x+X+4-2
= 3x+2
Figure HNMLKEFG is the image of figure ABCDKLMN after being rotated 90 degrees counter-clockwise around point K. Draw an auxiliary line in figure ABCDKLMN to create a quadrilateral. Draw the image of the auxiliary line when rotated 90 degrees counter-clockwise around point K. Write a congruence statement for the quadrilateral you created in figure ABCDKLMN and the image of the quadrilateral in figure HNMLKEFG.