Prove the following trigonometric identities.

$cosec θ \sqrt{1 - \cos^{2} θ} = 1$

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Solution

We know that,

So,

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(\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}

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

\frac{s i n 2 θ}{1 - c o s 2 θ} = c o t θ o r \frac{1 - c o s^{2} θ}{1 + c o s 2 θ} = \frac{t a n^{2} θ}{2}

\frac{{cos}^{2} θ}{{cot}^{2} θ - {cos}^{2} θ} = 3, 0^{\circ} < θ < 90^{\circ}

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