Prove the following trigonometric identities-1-cos-sin-sin- 1-cos-

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Complementary Trigonometric Ratios

Prove the fol...

Question

Prove the following trigonometric identities.

$\frac{1 - \cos θ}{\sin θ} = \frac{\sin θ}{1 + \cos θ}$

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\frac{\cos θ}{1 - \sin θ} = \frac{1 + \cos θ + \sin θ}{1 + \cos θ - \sin θ}

\frac{sinθ}{1 + cosθ} + \frac{(1 + cosθ)}{sinθ} = 2 cosecθ

\sqrt{\frac{\sec θ - 1}{\sec θ + 1}} + \sqrt{\frac{\sec θ + 1}{\sec θ - 1}} = 2 cosec θ

\sqrt{\frac{1 + \sin θ}{1 - \sin θ}} + \sqrt{\frac{1 - \sin θ}{1 + \sin θ}} = 2 \sec θ

\sqrt{\frac{1 + \cos θ}{1 - \cos θ}} + \sqrt{\frac{1 - \cos θ}{1 + \cos θ}} = 2 cosec θ

\frac{\sec θ - 1}{\sec θ + 1} = {(\frac{\sin θ}{1 + \cos θ})}^{2}

\frac{\sin θ + 1 - \cos θ}{\cos θ - 1 + \sin θ} = \frac{1 + \sin θ}{\cos θ}

\tan θ = \frac{1}{2}

(\frac{\cos θ}{\sin θ} + \frac{\sin θ}{1 + \cos θ})

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