Question

please solve the problem. wrong answer will be reported ​

Answer 1

$Given \: \alpha + \beta = 90\degree \: -- (1)$

$\implies \beta = 90\degree - \alpha \: --(2)$

$LHS = \red{ \frac{cos^{2} \alpha + cos^{2} \beta }{ sin^{2} ( \alpha + \beta ) } } \\= \frac{cos^{2} \alpha + cos^{2} (90 - \alpha) }{ sin^{2} 90\degree } \: [ From \: (1) \:and \:(2) ]$

$= \frac{ cos^{2} \alpha + sin^{2} \alpha }{1}$

_________________

We know that,

$1. sin 90\degree = 1 \\2. cos^{2} \alpha + sin^{2} \alpha = 1$

__________________

$\green {= 1 } \\= RHS$

$Hence \:proved$

♪••.