PYQ - Prove the following I — task. Maths TNSB Mentoring, Class 10 Crash course.

Verify whether \(\sqrt{\frac{1 + cos \B }{1 - cos \ B}} = cosec \ B + cot \ B\)

Proof:

Answer variants:

\(sec \ B\)

\(sin^{2} \ B\)

\(cot \ B\)

\(cos^{2} \ B\)

\(cosec \ B\)

\(tan \ B\)

\begin{array}{l} LHS = \sqrt{\frac{1 + \cos B}{1 - \cos B}} \\ = \sqrt{\frac{1 + \cos B}{1 - \cos B} \times \frac{1 + \cos B}{1 + \cos B}} \\ = \sqrt{\frac{{(1 + \cos B)}^{2}}{1 - \cos^{2} B}} \\ = \sqrt{\frac{{(1 + \cos B)}^{2}}{i}} \\ = \frac{1 + \cos B}{\sin B} \\ = = \frac{1}{\sin B} + \frac{\cos B}{\sin B} \\ = i + i \end{array}

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