Question

cos^(2)x=(cscxcosx)/(tanx+cotx)

Answer 1

$\cos^2 x = \dfrac{\csc x \cos x}{\tan x + \cot x}$

$\cos^2 x = \dfrac{\csc x \cos x}{\dfrac{\sin x}{\cos x} + \dfrac{\cos x}{\sin x}}$

$\cos^2 x = \dfrac{\csc x \cos x}{\frac{\sin x}{\cos x} \times \frac{\sin x}{\sin x} + \frac{\cos x}{\sin x} \times \frac{\cos x}{\cos x}}$

$\cos^2 x = \dfrac{\csc x \cos x}{\frac{\sin^2 x}{\sin x \cos x} + \frac{\cos^2 x}{\sin x \cos x}}$

$\cos^2 x = \dfrac{\csc x \cos x}{\frac{1}{\sin x \cos x}}$

$\cos^2 x = \csc x \cos x \sin x \cos x$

$\cos^2 x = \dfrac{1}{\sin x} \cos x \sin x \cos x$

$\cos^2 x = \cos^2 x$