Question

Prove the following trignometric identities:

$(1-co{s}^{2}A)cose{c}^{2}A=1$

Answer 1

By the trig identities

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

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

and

$cose{c}^2\theta$ = $\frac{1}{si{n}^2\theta }$

We have

$1-co{s}^2\theta$($cose{c}^2\theta$)

= $si{n}^2\theta$($\frac{1}{si{n}^2\theta }$)

= 1