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Question
If \[\sin A = \frac{4}{5}\], the value of \[\sqrt{\frac{1 - \cos(90^\circ - A)}{1 + \cos(90^\circ - A)}}\] is ______.
Options
1
3
\[\frac{1}{2}\]
\[\frac{1}{3}\]
MCQ
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Solution
\[\boldsymbol{\frac{1}{3}}\]
Explanation:
Given,
\[\sin A = \frac{4}{5}\]
We need to find the value of:
\[\sqrt{\frac{1 - \cos(90^\circ - A)}{1 + \cos(90^\circ - A)}}\]
Solving,
\[\Rightarrow \sqrt{\frac{1 - \cos(90^\circ - A)}{1 + \cos(90^\circ - A)}}\]
\[\Rightarrow \sqrt{\frac{1 - \sin A}{1 + \sin A}}\]
\[\Rightarrow \sqrt{\frac{1 - \frac{4}{5}}{1 + \frac{4}{5}}}\]
\[\Rightarrow \sqrt{\frac{\frac{5 - 4}{5}}{\frac{5 + 4}{5}}}\]
\[\Rightarrow \sqrt{\frac{\frac{1}{5}}{\frac{9}{5}}}\]
\[\Rightarrow \sqrt{\frac{1 \times 5}{5 \times 9}}\]
\[\Rightarrow \sqrt{\frac{1}{9}}\]
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