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

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Complementary Trigonometric Ratios

Prove the fol...

Question

Prove the following trigonometric identities.

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

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(i) \sqrt{\frac{1 + \sin θ}{1 - \sin θ}} = (\sec θ + \tan θ) (ii) \sqrt{\frac{1 - \cos θ}{1 + \cos θ}} = (cosec θ - \cot θ) (iii) \sqrt{\frac{1 + \cos θ}{1 - \cos θ}} + \sqrt{\frac{1 - \cos θ}{1 + \cos θ}} = 2 cosec 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) $(sin θ + cos θ) (tan θ + cot θ) = sec θ + cosec θ$

Prove the following trigonometric identities:

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

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 identity $\sqrt{\frac{1 - cos θ}{1 + cos θ}} = c o s e c θ - cot θ$

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