Answers
9514 1404 393
Explanation:
For proofs of this nature, it often works well to replace everything possible with appropriate equivalents. Here, we'll use sin² to represent sin²(A), and equivalent notation for other trig functions.
We will change the left side to the form of the right side.
[tex]\displaystyle \frac{\tan^2-\cot^2}{1+\cot^2}=\frac{\sin^2-\cos^2}{\cos^2}\\\\=\frac{(\sec^2-1)-(\csc^2-1)}{\csc^2}\\\\=(\sin^2)(\sec^2-\csc^2)\\\\=\frac{\sin^2}{\cos^2}-1=\frac{\sin^2-\cos^2}{\cos^2}\qquad\text{Q.E.D.}[/tex]
__
The equivalents (identities) used are ...
1+tan² = sec²
1+cot² = csc²
1/csc = sin
sec = 1/cos
Related Questions
1.
The width of a rectangle is 19 centimeters less than double the length.
Let v be length of the rectangle. Write a variable expression for the width.
Answers
Answer:
width = 2v - 19
Step-by-step explanation:
Monica worked 3.5 hours and is paid $10 per hour. How much did she make in 3.5 hours?
Answers
Answer:
She would make $35.
Step-by-step explanation:
If you do 10 x 3.5, you will get the answer of $35.
Answer:
$30
Step-by-step explanation:
She would be getting paid by the HOUR, and she has worked 3.5 hours. If she gets paid every HOUR, that means that she would be paid three times when working 3.5 hours. The answer would be $30.
The person who wrote the question might want $35 dollars as the answer, but logically the answer should be $30.
Write the equation of the line in fully simplifoed slope intercept form
Answers
Answer:
y = -⁵/₃x + 8Step-by-step explanation:
The equation of the line in slope-intercept form: y = mx + b, where m is a slope and b is y-intercept
Slope of line that passes through two given points: [tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
(0, 8) ⇒ x₁ = 0, y₁ = 8
(3, 3) ⇒ x₂ = 3, y₂ = 3
[tex]\bold{m=\dfrac{3-8}{3-0}=\dfrac{-5}3=-\dfrac53}[/tex]
b = 8
Therefore the equation: y = -⁵/₃x + 8
Drag fruit to represent each total weight shown.
Answers
3 strawberries in the second box
2 tomatoes (or whatever that is) in the third box
5/8 lb of fruit = 1/8+1/8+1/8+1/8+1/8=5/8
3/6 lb of fruit = 1/6+1/6+1/6=3/6
2/3 lb of fruit = 1/3+1/3=2/3
how many parts 1/6s does it take to name the same amount as 1/3
Answers
Answer:
Two 1/6 pieces
Step-by-step explanation:
Two 1/6 pieces equals 1/3 of the apple
So that will be 1/6 + 1/6 = 2/6
And 2/6 simplified is 1/3.
Is negative 40 greater than 12
Answers
Answer:
No, 12 is greater than -40
Step-by-step explanation:
Answer: I think your question is: Is negative forty greater than positive 12. It is not greater. Even if it was negative 40 and negative 12 it still would not be greater. Hope this helps :)
Step-by-step explanation:
What is the value of 3^2+4(2+4)x6 divided by 8+4
Answers
Answer:
its 31
Step-by-step explanation:
What is the GCF of the numerator & denominator below?
(x-2)(x+3)/x^2+4x+3
Answers
Answer:
Step-by-step explanation:
Factorize the denominator
Sum = 4
Product = 3
Factors = 1 , 3 {1*3 = 3 and 1+3 = 4}
x² + 4x + 3 = x² + x + 3x + 1*3
= x(x + 1) + 3(x + 1)
= (x + 1)(x + 3)
GCF of the numerator and denominator = (x + 3)
In ΔBCD, the measure of ∠D=90°, the measure of ∠B=22°, and DB = 44 feet. Find the length of BC to the nearest tenth of a foot.
Answers
Answer:47.5
Step-by-step explanation:
I need help on this plz thanks
Answers
Answer:
its a black screen
Step-by-step explanation:
Write and solve a proportion to answer the question.
75% of 124 is what number a
?
Write and solve a proportion to answer the question.
72 is what percent of 45?
Answers
(75:100)*124 =
(75*124):100 =
9300:100 = 93
72÷45×100
= 160
need help ASAP !!!
[tex] \sqrt{6854 \times 6854} [/tex]
Answers
Answer:
√{6854×6854}=√6854²=±6854 is your answer
Answer:
[tex]±6854 [/tex]
Step-by-step explanation:
[tex] \sqrt{6854 \times 6854} [/tex]
[tex] \sqrt{ {6854}^{2} } [/tex]
[tex]±6854 .[/tex]
Multiply: 7,277x6
Please hurry!
Answers
43662 dude. .........ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ
I need help with finding x. Can someone help me please?
Answers
Answer:
There isn't the picture :c
Horace measured a circular lid and found d, the diameter, was 8 inches and C, the circumference, was 25 inches. Which expression represents an approximate value for p?
Answers
Horace measured a circular lid and found d, the diameter, was 8 inches and C, the circumference, was 25 inches. Which expression represents an approximate value for pi?
Answer:
pi = 3.125
Step-by-step explanation:
We are given;
Diameter; d = 8 inches
Circumference; C = 25 inches
Formula for circumference of a circle is;
C = πd
We are trying to find the value for pi(π)
Thus; π = C/d
π = 25/8
π = 3.125
what is -1 3/10 + -3.8
Answers
Answer:
answer
Step-by-step explanation:
=convert 3.8 into mixed number
=3 4/5
=1 3/10+3 4/5
=5.1 in mixed fraction
=5 1/10
if i got it wrong i am seriously sorry!
b Two quadrilaterals both have angles 55°, 65°, 95º and 145º
Felix says, 'The two quadrilaterals are similar.
True or false? Explain why.
Answers
Answer:
I say true.
Step-by-step explanation:
cuz both of the quadrilaterals have the same angles and all angles equal 360 °
Andrew cut 24 feet of chain into pieces that were each 1/3ft long. How many of these pieces did Andrew have after cutting the chain?
Answers
Answer:
72
Step-by-step explanation:
1/3 ft is 4 inches
24 feet is 288 inches
take 288 and divide it by 4
you get 72, which is the number of pieces of chain Andrew has
Rounded to the nearest hundredth, what is the positive solution to the quadratic equation 0=2x^2+3x-8? 1.99 2.00
Answers
Answer:
1.39
Step-by-step explanation:
Given the quadratic equation :
2x^2+3x-8 = 0
We could apply the quadratic equation formula :
a = 2 ; b = 3, c = - 8
The formula is stated as :
-b±sqrt(b² - 4ac)/2a
To save computation tune, we could use a calculator :
The roots are : - 2.886 ; 1.386
The positive solution rounded to the nearest hundredth is : 1.39
11. Bethany is paid 4% commission on
carpet sales. She sold $850 worth of
carpet to a family today. What was
her commission?
Answers
The shaded portion of the bar model in Part A shows 38. What percent is equivalent to 38? Enter the correct answer in the box.
Answers
Question:
The shaded portion of the bar model in Part A shows 3/8. What percent is equivalent to 3/8? Enter the correct answer in the box.
Answer:
The equivalent is 37.5%
Step-by-step explanation:
Given
[tex]\frac{3}{8}[/tex]
Required
The equivalent
The model is not shown, but the question can still be solved.
We have:
[tex]\frac{3}{8}[/tex]
Multiply by 100%
[tex]\frac{3}{8} = \frac{3}{8} * 100\%[/tex]
[tex]\frac{3}{8} = 0.375 * 100\%[/tex]
[tex]\frac{3}{8} = 37.5\%[/tex]
Hiiiooo can someone please help me ❤️❤️:D
Answers
Answer:
10
Step-by-step explanation:
because it shows where the line is
Can you help me with this one to
Answers
Answer:
3 and 5 but i dont know what number goes in what picture so just try then try the other way round if its wrong
Step-by-step explanation:
Answer:
Purple Diamond = 2 Green Moon = 7.5 Pink Trapezium = 30
Step-by-step explanation:
T = Pink Trapezium
D = Purple Diamond
M = Green Moon
Line 1 = T = 30 x 1 = 30
Line 2 = (D x D) x (M) = (2x2) x (7.5) = 4 x 7.5 = 30
The key is the weight of the line multiples to 30
Just like graphs do with x/y
If x is horizontal then y is vertical
= x/y we get the gradient which is the same as division or dividing 30/30 = 1 being the base weight amount
and same as 30/7.5 = 4 and simplifying 4 to (2 x 2)that means an easier way to see the number of (2x2) being the base weight = 1 x 2 then 1 x 2 then as we have found 4 its simplification we can divide it into 30 to show 30/4 = 7.5 for the Moon or for (M) above.
The 4 number is simplification and (+ 2 )(+ 2) is its factorization before it turns to 30 to show 30 = (2 x 2 x 7.5) or 2^2 x 7.5 = 30. Etc. Etc.
I need the answer in under 34 min
Answers
Answer:
I. 1 cup is $4.50
2 cups is $9.00
3 cups is $13.50
ll. 6 cups is $27.00
Step-by-step explanation:
Now since the number of cups is proportional to the total cost of frozen yoghurt,and the cost of 4 yoghurts cups where given .ie. $18.00
then 1 cup is $18/4 which is $4.50 per one cup, thus the other cost of cups are given.
therefore 6 cups is 6•18/4 which is $27.00.
hence 5 cups is 5•18/4 which is $22.50.
Write down in terms of n, an expression for the nth term
of the following sequences:
a) 4 1 -2 -5 -8
b) -7 -12 -17 -22 -27
Answers
Step-by-step explanation:
This the answer in the photo
WILL GIVE BRAINLIEST!
Given that ℓ1 ∥ ℓ2 and y = 36°, find x.
x =
Answers
Answer:
x = 48
Step-by-step explanation:
From the given diagram, the sum of the angles given is equal to 180 degrees as shown;
x+y+2x = 80
Since y = 36
x +36+2x = 180
3x = 180 - 36
3x = 144
x = 144/3
x = 48
Hence the value of x is 48
2. Suppose y varies directly as x and y=-8 when x=-2. Find x when y=32.
Answers
Answer:
x = 8
Step-by-step explanation:
Use the direct variation equation, y = kx
Plug in the given values of x and y, and solve for k:
y = kx
-8 = k(-2)
4 = k
So, the equation is y = 4x
Using this, plug in 32 as y, and solve for x:
y = 4x
32 = 4x
8 = x
So, x = 8 when y = 32
Order the sides or angles of each triangle from least to greatest.
Answers
Answer:
SU , UT , ST
Step-by-step explanation:
asap 50 points!
-3xy = what when x=5 and y= -6
answers :
-90
90
-33
33
Answers
Answer:
I think its 33
Step-by-step explanation:
i may be wrong
Answer:
choice 2) 90
Step-by-step explanation:
-3xy = ?
x=5 and y= -6
-3(5)(-6) = 90
please help me with my math
Answers
Answer:
SA = 480 cm²
Step-by-step explanation:
Surface area of the composite figure given in the picture = (Surface Area of the triangular prism on the top - area of the rectangular base) + (Surface area of the rectangular prism - Area of the rectangular base)
Surface area of the triangular prism = Area of the triangular bases + (perimeter of the base × Height)
= [tex]2(\frac{1}{2}\times 3\times 8)[/tex] + [(5 + 5 + 8)×12]
= 24 + 216
= 240 cm²
Area of the rectangular surface of the prism = 8 × 12 = 96 cm²
Surface area of the rectangular prism = 2(lb + bh + hl)
Here, l = Length, b = width and h = Height of the rectangular prism
= 2(8 × 12 + 12 × 6 + 6 ×8)
= 432 cm²
Surface area of the composite figure = (240 - 96) + (432 - 96)
= 144 + 336
= 480 cm²