Question

Prove the following trignometric identities:

$co{s}^{2}A+\frac{1}{1+co{t}^{2}A}=1$

Answer 1

We know that,

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

$cose{c}^2\theta -co{t}^2\theta =1$

So, $co{s}^{2}A+\frac{1}{1+co{t}^{2}A}=co{s}^{2}A+\frac{1}{cose{c}^{2}A}$

=$co{s}^{2}A+\frac{1}{(cosecA{)}^2}$ = $co{s}^2\theta +si{n}^2\theta$

= 1