Question

If \[\sin A = \frac{4}{5}\], the value of \[\sqrt{\frac{1 - \cos(90^\circ - A)}{1 + \cos(90^\circ - A)}}\] is ______.

पर्याय

• 1

• 3

• \[\frac{1}{2}\]

• \[\frac{1}{3}\]

Answer 1

\[\boldsymbol{\frac{1}{3}}\]

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,

\[\Rightarrow \sqrt{\frac{1 - \cos(90^\circ - A)}{1 + \cos(90^\circ - A)}}\]

\[\Rightarrow \sqrt{\frac{1 - \sin A}{1 + \sin A}}\]

\[\Rightarrow \sqrt{\frac{1 - \frac{4}{5}}{1 + \frac{4}{5}}}\]

\[\Rightarrow \sqrt{\frac{\frac{5 - 4}{5}}{\frac{5 + 4}{5}}}\]

\[\Rightarrow \sqrt{\frac{\frac{1}{5}}{\frac{9}{5}}}\]

\[\Rightarrow \sqrt{\frac{1 \times 5}{5 \times 9}}\]

\[\Rightarrow \sqrt{\frac{1}{9}}\]