Show how to prove that the first expression is identical to the second expression.?

First expression: (1-tan^2 theta)/(1+sin^2 theta)

Second expression: (2/cos^2 theta) - 1

(1-tan^2 theta)/(1+sin^2 theta)(2/cos^2 theta) - 1

1 Answer
Apr 1, 2018

color(red)((1-tan^2(theta))/(1+sin^2(theta))!=(2/cos^2(theta))-1

Explanation:

(1-tan^2(theta))/(1+sin^2(theta))=(2/cos^2(theta))-1

Let \ \ \ \ theta=pi/3

(1-tan^2(pi/3))/(1+sin^2(pi/3))=(2/cos^2(pi/3))-1

(-2)/(7/4)=2/(1/4)-1

-8/7=7color(white)(88) This is false

Therefore:

color(red)((1-tan^2(theta))/(1+sin^2(theta))!=(2/cos^2(theta))-1