Prove that- - -cos- - cos- - cosec- -1cosec- - 1

θ cosθθ + cosθ⇒cosθsinθ cosθcosθsinθ+cosθ⇒cosθ(1sinθ 1)cosθ(1sinθ+1)⇒θ 1θ+1 ...

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General Solution of Trigonometric Equation

Prove that: ...

Question

Prove that: $\frac{cot θ - cos θ}{cot θ + cos θ} = \frac{c o s e c θ - 1}{c o s e c θ + 1}$

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\frac{sin θ}{1 - cos θ} = c o s e c θ + cot θ

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

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

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

\frac{(p^{2} - 1)}{(p^{2} + 1)} .

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