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What is \(\sqrt {\frac{{1 + sin\theta }}{{1 - sin\theta }}}\) equal to?1). sec θ – tan θ2). sec θ + tan θ3). cosec θ + cot θ4). cosec θ – cot θ |
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Answer» $(\begin{ARRAY}{l} \Rightarrow \;\sqrt {\frac{{1 + SIN\theta }}{{1 - sin\theta }}} \; = \;\sqrt {\frac{{1 + sin\theta }}{{1 - sin\theta }}\; \TIMES \;\frac{{1 + sin\theta }}{{1 + sin\theta }}} \; = \;\sqrt {\frac{{{{\left( {1 + sin\theta } \right)}^2}}}{{1 - {{\sin }^2}\theta }}} \; = \;\frac{{1 + sin\theta }}{{cos\theta }}\; = \;\frac{1}{{cos\theta }} + \frac{{sin\theta }}{{cos\theta }}\; = \;sec\theta+ tan\theta \\\THEREFORE \;\sqrt {\frac{{1 + sin\theta }}{{1 - sin\theta }}} \; = \;sec\theta+ tan\theta\end{array})$ |
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