Answers
Answer:
See Below.
Step-by-step explanation:
We want to verify the equation:
[tex]\displaystyle \frac{\tan\theta}{ 1- \cot \theta} + \frac{\cot\theta}{1 - \tan\theta} = \frac{\dfrac{\sin\theta}{\cos\theta}}{1 - \dfrac{\cos\theta}{\sin\theta}} + \frac{\dfrac{\cos\theta}{\sin\theta}}{1 - \dfrac{\sin\theta}{\cos\theta}}[/tex]
Recall that tanθ = sinθ / cosθ. Likewise, cotθ = cosθ / sinθ. Then by substitution:
[tex]\displaystyle \begin{aligned} \frac{\tan\theta}{ 1- \cot \theta} + \frac{\cot\theta}{1 - \tan\theta} & = \frac{\dfrac{\sin\theta}{\cos\theta}}{1 - \dfrac{\cos\theta}{\sin\theta}} + \frac{\dfrac{\cos\theta}{\sin\theta}}{1 - \dfrac{\sin\theta}{\cos\theta}} \\ \\ & \stackrel{\checkmark}{=} \frac{\dfrac{\sin\theta}{\cos\theta}}{1 - \dfrac{\cos\theta}{\sin\theta}} + \frac{\dfrac{\cos\theta}{\sin\theta}}{1 - \dfrac{\sin\theta}{\cos\theta}} \end{aligned}[/tex]
Hence verified.
Given :
tan∅/1-cot∅ + cot∅/1-tan∅ = sin∅/cos∅ ÷ (1- cos∅/sin∅ ) + cos∅/sin∅ ÷ (1 - sin∅/cos∅)To Do :-
To prove LHS = RHSProof :-
We know that ,
sin∅/cos∅ = tan∅cos∅/sin∅ = cot∅On using above two in LHS ,
LHS = tan∅/1-cot∅ + cot∅/1-tan∅LHS = tan∅/1-cot∅ + cot∅/1-tan∅ = sin∅/cos∅ ÷ (1- cos∅/sin∅ ) + cos∅/sin∅ ÷ (1 - sin∅/cos∅) LHS = RHSHence proved !
Related Questions
Let f(x)=x^2-4 and h(x) =x-5 find (f-h) (2)
Answers
9514 1404 393
Answer:
(f -h)(2) = 3
Step-by-step explanation:
(f -h)(2) = f(2) -h(2) = (2^2 -4) -(2 -5) = 0 -(-3)
(f -h)(2) = 3
The daily change in barometic pressure for 4 days are: .05, .09, .04, and .18 inches. What is the mean change?
Answers
Answer:
It means like swicthing up thing 09, 18, 04
Step-by-step explanation:
If there is a 75 x 50 hardwood top and bottom rail in this fence to connect the posts, how many 5.4 m long lengths of timber rail are needed to build the fence? No. of lengths 05 -
Answers
Answer:
3,750
Step-by-step explanation:
because you need to do 7 * 75 * 50 and you will get the answer but it will be 3007 715 so that would be 7 3750h fences
solve pls brainliest
Answers
Answer:
2n-61
twice a number means 2 x n
61 less is just subtracting 61
Hi there!
»»————- ★ ————-««
I believe your answer is:
[tex]2n - 61[/tex]
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
Twice a number means that a number would be multiplied two times. '61 less than XYZ' means that 61 would be taken away from XYZ.⸻⸻⸻⸻
"61 less than twice a number" would be: 2n - 61
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
HELP IM GIVING 20 BRAINLEIST PLZZZ
Answers
Answer:
oh no I don't no the answer boss and
I have a idea to solve this
kanna Sprite kudi answere yosi
Answer:
f(0) = -1
f(1) = 2
f(2) = 4
Step-by-step explanation:
umm math
Write an equation that expresses the relationship. Use k as the constant of variation.
x varies inversely as m.
Answers
Step-by-step explanation:
x = k/m
hope this helps. good luck!
Increase 100kg by 10%
Answers
Answer:
110 kg
Step-by-step explanation
a simple way is to just do 100 plus 10= 110
Here is a table of daily births of babies (per 100,000 people) for 12 of the most populous states in the US.
State
Daily births (per 100,000 people)
California
292
Texas
556
New York
288
Florida
28
Illinois
299
Pennsylvania
135
Ohio
193
Georgia
334
Michigan
239
North Carolina
130
New Jersey
214
Virginia
27
Assume that σ = 216.83 for the entire population of the United States. Calculate the standard error.
Answers
Answer:
uhhhh can you simplify better and show the actual graph
Step-by-step explanation:
-2x+y=1 solve with steps
Answers
Answer:
x=1 and y=3
Step-by-step explanation:
-2x1=-2
-2+3=1
So this answer makes sense
Answer:
y = 2x + 1
Step-by-step explanation:
Given: -2x+y=1
Add 2x to both sides: y=1+2x
Reorder: y = 2x + 1
I am not sure exactly what you need for this point, but here is the equation in y=mx+b form aka slope-intercept form
m = slope = 2
b = y-intercept = 1
Hope this helps, have a nice day :D
HELP! find the value of x
Answers
Answer:
x = 12°
Step-by-step explanation:
To find the value of x, you have to subtract 65 from 180.
This is because angles on a straight line add upto 180 degrees, and 65 is the supplementary angle of 11x -17.
Hence,
11x - 17 + 65 = 180
11x + 48 = 180
11x = 132
x = 12
Hope this helps and be sure to have a wonderful time ahead at Brainly! :D
find the distance between (2,4) and (-2,-4)
Answers
Answer:
[tex]8.9444 = \sqrt{80} [/tex]
Step-by-step explanation:
the distance is equal to the magnitude or modulus of the vector between the coordinates,
to find the distance, find the vector then the magnitude,ie
vector=
[tex] \frac{4}{2} - \frac{ - 4}{ - 2 } = \frac{8}{4} [/tex]
distance=
[tex] | \sqrt{{8}^{2} + {4}^{2} } | = | \sqrt{64 + 16 } | \\ | \sqrt{80 } | = \sqrt{80} = 8.944[/tex]
kindly give me a brainliest
Simplify by rationalizing the denominator.
(4√15)/√5
Answers
The simplified form of the numerical expression (4√15) / √5 will be 4√3.
What is the value of the expression?When the relevant factors and natural laws of a mathematical model are given values, the outcome of the calculation it describes is the expression's outcome.
The ratio is given below.
⇒ (4√15) / √5
Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction are all part of the PEMDAS formula. To answer the problem properly and accurately, this rule must be followed.
⇒ (4√15) / √5
⇒ [4 × √(3 x 5)] / √5
⇒ (4 × √3 × √5) / √5
⇒ 4 × √3
⇒ 4√3
The simplified form of the numerical expression (4√15) / √5 will be 4√3.
More about the value of the expression link is given below.
brainly.com/question/23671908
#SPJ5
multiplacation of fractions
c solve (3/9) (-2/3) =
explain
Answers
Step-by-step explanation:
(3/9) × (-2/3
=> {3×(-2)}/(9×3)
=> (-6/27). Ans.
Or
(3/9) × (-2/3)
=> -2/9 Ans.
Evaluate f(x)=x+6 when x = -2, 0, and 5.
Answers
Answer:
f(5) = 11 , f(0) = 6 , f(-2) = 4
Given expression:
f(x) = x + 6
Find:
f(−2), f(0), f(5)
Computation:
f(x) = x + 6
When x = -2
f(-2) = -2 + 6
f(-2) = 4
When x = 0
f(0) = 0 + 6
f(0) = 6
When x = 5
f(5) = 5 + 6
f(5) = 11
Step-by-step explanation:
Kyle collects rainwater in two barrels. Last week one barrel collected 1.46 gallons of rainwater. The other barrel collected 0.751 gallon of rainwater.
What was the total amount of rainwater that Kyle collected last week?
Answers
Answer:
2.211 gallon of rainwater
Step-by-step explanation:
1.46 gallon + 0.751 gallon = 2.211 gallon
10. The table below shows coordinate points
that model a proportional relationship. What is
the missing value in the table?
х
0
1
1.5
2
3
5
?
y
0
A. 4.5
B. 5
C. 6
D. 7.5
Answers
Answer:
— The table below shows coordinate points that model a proportional relationship. What is the missing value in the table? х 0 1 1.5 2 3 5 ? y
Step-by-step explanation:
Math Question For Math00999
Answers
most people lose 100 to 200 hairs per.day if you were to.lose 150 hairs per day for 10 days what would be the change in the numbers of hair you have
Answers
use the distributive property to write an expression that is equivelent to 8(a+4).
8(a+4) = ___ a + ____
Answers
Expand 8(a+4)
Hence, 8a + 32
I need help please thanks
Answers
Can someone help with a step by step?
Answers
Answer:
Pick option a and then write this in the box --> x^3(x - 1) (x - 83)
Step-by-step explanation:
x^5 − 84x^4 + 83x^3
= x^3(x - 1) (x - 83)
Answer:
x^3(x - 1) (x - 83)
Step-by-step explanation:
option a
Robert played baseball 14 times. Each time he played, he used 4 yellow balls and 3 white balls
Answers
Given the points (7, 6) and (-3, -4) find the slope.
Answers
Dan is 2 times the age of Thomas the sum of ages is 75 what is thomas age
Answers
Answer:
25
Step-by-step explanation:
thomas age = x
2x + x = 75
3x = 75
x = 25
Answer: Dan is 50, Thomas is 25
Step-by-step explanation: 75 divided by 3 = 25. 75 - 25 is 50
Which equation has the correct sign on the product?
O A. (-9)(-8)= -72
O B. 35(-5) = -175
O C. 13.3 =-39
O D. (-15)4 = 60
No links plsss:()
Answers
Answer:
B
Step-by-step explanation:
(+)x(-)=(-)
(-)x(-)=(+)
Estimate -4 2/3 x (2 1/4) + 3 5/6
Answers
Step-by-step explanation:
[tex] \tt{} - 4 \frac{2}{3} \times (2 \frac{1}{4} ) + 3 \frac{5}{6} [/tex]
[tex]\tt{} - \frac{14}{3} \times \frac{9}{4} + \frac{23}{6} [/tex]
[tex]\tt{} - 7 \times \frac{3}{2} + \frac{23}6[/tex]
[tex]\tt{} - \frac{21}{2} + \frac{23}{6} [/tex]
[tex]\tt{} - \frac{20}{3} [/tex]
[tex]\tt{} - 6 \frac{2}{3} [/tex]
Simplify
5(x + 3) - x + 2
Answers
Answer:
[tex]4x+17[/tex]
Step-by-step explanation:
1) Distribute
[tex]5(x+3)-x+2\\5x+15-x+2[/tex]
2) Add the numbers
[tex]5x+15-x+2\\5x+17-x[/tex]
3) Combine like terms
[tex]5x+17-x\\4x+17[/tex]
Answer:
4x+17
Step-by-step explanation:
So first we are going to have to use the distributive property
so
5*x and 5*3
Which is
5x and 15
So then we have,
5x+15-x+2
Now we just combine like terms
=4x+17
Hope this helps!! :)
Good Stuff is giving away free pens to each of the first 500 people who come in the store today. In the first hour, they gave away 30% of the pens. How many is this?
Answers
Answer:
150 pens given away
Step-by-step explanation:
10% of 500 is 50
50x3=150
500-150=350
PLS HELP WILL MARK BRAINLIEST!! TY
Answers
Answer: x=23
Step-by-step explanation:
180=(3x+18)+93
x=23
Answer:
x = 23°
Step-by-step explanation:
(180° - 93° - 18°) ÷ 3 = (87° - 18°) ÷ 3
= 69° ÷ 3
= 23°
your welcome :)
Which graph represents the System of inequalities shown below? y < -2x + 2
y > x - 1
Answers
Answer:
The second one (Top right)