question_answer

If \[\sin \,A=\frac{4}{5}\], then the value of \[\frac{1-\sin A}{1+\cos A}\]is

A) \[\frac{1}{8}\]

B) \[\frac{1}{2}\]

C) 2

D) \[\frac{3}{5}\]

Correct Answer: A

Solution :

Given, \[\sin \,A=\frac{4}{5}=\frac{BC}{AC}\]

Let \[BC=4k,\,AC=5k\]

Apply Pythagoras theorem,

\[A{{B}^{2}}+B{{C}^{2}}=A{{C}^{2}}\]

\[\Rightarrow \,\,A{{B}^{2}}+{{\left( 4k \right)}^{2}}={{\left( 5k \right)}^{2}}\]

\[\Rightarrow \,AB=\sqrt{25-16}=3\]

\[\Rightarrow \frac{1-\sin \,A}{1+\cos A}=\frac{1-\frac{4}{5}}{1+\frac{3}{5}}\]

\[=\frac{\left( 5-4 \right)}{5}\times \frac{5}{\left( 5+3 \right)}=\frac{1}{8}\]