Prove the following trigonometric identities-1- 2 - 1-cosec-cosec-

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Complementary Trigonometric Ratios

Prove the fol...

Question

Prove the following trigonometric identities.

$1 + \frac{\cot^{2} θ}{1 + cosec θ} = cosec θ$

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

\frac{c o s e c θ}{c o s e c θ - 1} + \frac{c o s e c θ}{c o s e c θ + 1} = 2 {sec}^{2} θ

Prove the following trignometric identities:

$\sqrt{\frac{1 - c o s θ}{1 + c o s θ}} = c o s e c θ - c o t θ$

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

1 + \frac{\cot^{2} θ}{(1 + cosecθ)} = cosecθ

1 + \frac{\tan^{2} θ}{(1 + secθ)} = secθ

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