How do you prove $sin^2theta - tantheta/ cos^2theta - cot^2theta = tan^2theta$ ?

Question

2786 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-03-21T00:28:45

The identity is false.

The given equation is not true for all $theta$ . For example, take $theta = pi/4$ . Then we have

$sin^2(theta)-tan(theta)/cos^2(theta)-cot^2(theta) = 1/2 - 2 - 1 = -5/2$

but

$tan^2(theta) = 1$

How do you prove sin^2theta - tantheta/ cos^2theta - cot^2theta = tan^2theta sin^2theta - tantheta/ cos^2theta - cot^2theta = tan^2theta?