Prove that - 1 - sin 2 x- cos 2x1 - sin 2x - cos 2x - x

1+sin 2x+cos 2x1+sin 2x cos 2x=(1+cos 2x)+sin 2x(1 cos 2x)+sin 2x =2cos ^2x+2sin xcos x2sin ^2x+2sin xcos x =2cos x(cos x+sin x)2sin x(sin x+cos ...

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Prove that : $\frac{1 + sin 2 x + cos 2 x}{1 + sin 2 x - cos 2 x} = cot x$

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\frac{1 - \cos 2 x + \sin 2 x}{1 + \cos 2 x + \sin 2 x} = \tan x

cos 2 x = {cos}^{2} x - {sin}^{2} x

sin 2 x = 2 sin x cos x

tan 2 x = \frac{2 tan x}{1 - {tan}^{2}}

\frac{1 + s i n 2 x}{c o s 2 x} = t a n (\frac{π}{4} + x)

Prove that

(i) $\frac{sin 2 x}{1 - cos 2 x} = cot x$

(ii) $\frac{1 - cos2x}{1 + cos 2 x} = {tan}^{2} x$

cos x + {cos}^{2} x = 1

{sin}^{2} x + {sin}^{4} x = 1

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