Prove that - 1-sin x-2cos 2 - 4 - x 2

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Prove that : ...

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Prove that : $1 + sin x = 2 {cos}^{2} (\frac{π}{4} - \frac{x}{2})$

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Prove that $\sqrt{\frac{1 + sin x}{1 - sin x}} = tan (\frac{π}{4} + \frac{x}{2})$

{cot}^{- 1} (\frac{\sqrt{1 + sin x} + \sqrt{1 - sin x}}{\sqrt{1 + sin x} - \sqrt{1 - sin x}}) = \frac{x}{2}; x \in (0, \frac{π}{4}) .

Prove that:

$2 {sin}^{2} \frac{3 π}{4} + 2 {cos}^{2} \frac{π}{4} + 2 {sec}^{2} \frac{π}{3} = 10$

2 {sin}^{2} \frac{3 π}{4} + 2 {cos}^{2} \frac{π}{4} + 2 {sec}^{2} \frac{π}{3} = 10

Prove that $\frac{cos x}{(1 - s i n x)} = t a n (\frac{π}{4} + \frac{x}{2})$

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