Question

Prove the following trignometric identities:

$ta{n}^2\theta co{s}^2\theta =1-co{s}^2\theta$

Answer 1

We know ,

$si{n}^2\theta +co{s}^2\theta$ = 1

So,

$ta{n}^2\theta co{s}^2\theta$ = ($tan\theta cos\theta {)}^2$

=($\frac{sin\theta }{cos\theta }cos\theta {)}^2$ = ($sin\theta {)}^2$ = $si{n}^2\theta$ = 1 - $co{s}^2\theta$