Question

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Answer 1

Answer:

see the explanation

Step-by-step explanation:

$\sqrt{\frac{\mathtt{1 - cos \theta}}{\mathtt{1 + cos \theta}}}$

By multiplying L.H.S. and R.H.S. with [1 - cosθ]. We get,

$\implies \sqrt{\frac{(1-cos\theta )}{(1+cos\theta)} \times \frac{( 1 - cos\theta)}{(1-cos\theta)}}$

$\implies \sqrt{\frac{(1-cos\theta )^2}{(1- cos^2 \theta )}}$

$\implies \sqrt{\frac{(1-cos\theta )^2}{(sin^2\theta)}}$

$\implies \frac{(1 - cos\theta)}{(sin\theta)}$

$\implies (\frac{1}{sin\theta} ) - (\frac{cos\theta}{sin\theta})$

$\implies \underline{\bold{cosec\theta - cot\theta}}$

                                             Hence Proved.

Answer 2

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