Question

Prove the following : ​

Answer 1

Step-by-step explanation:

IMPORTANT POINTS TO KNOW

$\cos(\pi + x) = - \cos(x) \\ \cos( - x) = \cos(x) \\ \sin(\pi - x) = \sin(x) \\ \cos( \frac{\pi}{2} + x ) = - \sin(x)$

WE GET THIS VALUES BY KNOWING WHAT ARE QUADRANTS AND IN WHICH WAY THE GIVEN FUNCTION CHANGES TO OTHER FUNCTION THIS WILL BE EXPLAINED YOUR CLASS TEACHERS PERFECTLY I THINK SO

NOW BY SUBSTITUTING THE GIVEN VALUES IN THE L.H.S WE GET

$\frac{ - \cos(x) \times \cos(x) }{ \sin(x) \times - \sin(x) } = \frac{ { \ \: (cos(x)) }^{2} }{ { \ \: (sin(x) }^{2}) }$

hence cos/sin is cot

$= > ( { \cot(x) })^{2} = rhs$

hence prooved thanks for your beautiful question