All categories

3 years ago

Prove that:- (1-sinA)(1+sinA)÷(1+cosA)(1-cosA)=cot^2A

Mathematics

1 answer:

astraxan [27]3 years ago

6 0

Answer:

see explanation

Step-by-step explanation:

Using the trigonometric identity

sin²x + cos²x = 1 , then

sin²x = 1 - cos²x and cos²x = 1 - sin²x

Consider the left side

$\frac{(1-sinA)(1 + sinA)}{(1+cosA)(1-cosA)}$ ← expand numerator/denominator using FOIL

= $\frac{1-sin^2A}{1-cos^2A}$

= $\frac{1-(1-cos^2A)}{1-(1-sin^2A)}$

= $\frac{1-1+cos^2A}{1-1+sin^2A}$

= $\frac{cos^2A}{sin^2A}$

= cot²A = right side , thus proven

You might be interested in

You are painting all four walls of a shed. Each wall is a rectangle with a length of 14 feet and a height of 8 feet. A gallon of

Setler [38]

It's 448 square feet so you'll require 1 and some. buy 2 gallons

7 0

4 years ago

Does someone that knows how to do this??

mezya [45]

Answer:

-1/2

Step-by-step explanation:

rise over run

rise is -2

run is 4

(-2/4)/2=(-1/2)

hope this helps :3

if it did pls mark brainliest

6 0

3 years ago

Any athlete who fails the Enormous State University's women's soccer fitness test is automatically dropped from the team. Last y

castortr0y [4]

Using conditional probability, it is found that there is a 0.7873 = 78.73% probability that Mona was justifiably dropped.

Conditional Probability

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

P(B|A) is the probability of event B happening, given that A happened.
$P(A \cap B)$ is the probability of both A and B happening.
P(A) is the probability of A happening.

In this problem:

Event A: Fail the test.
Event B: Unfit.

The probability of <u>failing the test</u> is composed by:

46% of 37%(are fit).
100% of 63%(not fit).

Hence:

$P(A) = 0.46(0.37) + 0.63 = 0.8002$

The probability of both failing the test and being unfit is:

$P(A \cap B) = 0.63$

Hence, the conditional probability is:

$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.63}{0.8002} = 0.7873$

0.7873 = 78.73% probability that Mona was justifiably dropped.

A similar problem is given at brainly.com/question/14398287

3 0

3 years ago

A theater charges $50 per ticket for seats in section a, $40 per ticket for seats in section b, and $20 per ticket for seats in

alukav5142 [94]

The first thing we must do for this case is to define variables.
We have then:
x: ticket for seats in section a
y: ticket for seats in section b
z: ticket for seats in section c
We write the system of equations:
50x + 40y + 20z = 335000
x + y + z = 9500
y = x + z + 500
Solving the system we have:
x = 1500
y = 5000
z = 3000
Answer:
ticket for seats in section a = 1500
ticket for seats in section b = 5000
ticket for seats in section c = 3000

7 0

3 years ago

How to solve this problem

Simora [160]

Say x is the number of books third graders read, the equation would be;

x + 2599 = 4628

to solve;
x = 4628 - 2599
x = 2029 books third graders read

8 0

3 years ago

Prove that:- (1-sinA)(1+sinA)÷(1+cosA)(1-cosA)=cot^2A​

Prove that:- (1-sinA)(1+sinA)÷(1+cosA)(1-cosA)=cot^2A