Question

This one is also of trigonometry please answer step by step with a attachment

Answer 1

Question :-

Prove that

$\sin {}^{4} (x) \times cosec {}^{2} (x) + \cos {}^{2} (x) \times \sec {}^{2} (x) = 1$

Solution :-

Take LHS

$\sin {}^{4} (x) \times cosec {}^{2} (x) + \cos {}^{4} (x) \times \sec {}^{2} (x) \\ \\ as \\ \cosec(x) = \frac{1}{ \sin(x) } \\ \\ and \sec(x) = \frac{1}{ \cos(x) }$

Hence,

$\sin {}^{4} (x) \times \frac{1}{ \sin {}^{2} (x) } + \cos {}^{4} (x) \times \frac{1}{ \cos {}^{2} (x) } \\ \\ \sin {}^{2} (x) + \cos {}^{2} (x)$

We know that

$\sin {}^{2} (x) + \cos {}^{2} (x) = 1$

Hence,

$1 = 1$

LHS =RHS - - - (PROVED)