Prove the following trigonometric identities- 2-1cosec2-1-1

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Complementary Trigonometric Ratios

Prove the fol...

Question

Prove the following trigonometric identities.

(sec² θ − 1) (cosec² θ − 1) = 1

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{cot}^{2} θ - \frac{1}{{sin}^{2} θ} = - 1

Prove the following trigonometric identities:

$\frac{(1 + c o t^{2} θ) t a n θ}{s e c^{2} θ} = c o t θ$

\frac{1 + \sin θ}{\cos θ} + \frac{\cos θ}{1 + \sin θ} = 2 \sec θ

Prove the following trignometric identities:

$(s e c^{2} θ - 1) (c o s e c^{2} θ - 1) = 1$

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

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