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

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Derivative of Some Standard Functions

Prove the fol...

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Prove the following trigonometric identities.

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

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Prove the following trigonometric identities.
(i) $\frac{1 + cos θ + sin θ}{1 + cos θ - sin θ} = \frac{1 + sin θ}{cos θ}$

(ii) $\frac{sin θ - cos θ + 1}{sin θ + cos θ - 1} = \frac{1}{sec θ - tan θ}$

(iii) $\frac{cos θ - sin θ + 1}{cos θ + sin θ - 1} = cosec θ + cot θ$

(iv) $(sin θ + cos θ) (tan θ + cot θ) = sec θ + cosec θ$

\frac{cot θ - cos θ}{cot θ + cos θ} = \frac{cosec θ - 1}{cosec θ + 1}

Prove the following trigonometric identities:

$\frac{1 + s e c θ}{s e c θ} = \frac{s i n^{2} θ}{1 - c o s θ}$

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