Question

If $A={45}^o,B={30}^o$ then $\frac{\sin A}{\cos A+\sin A.\sin B}=$

• A. $\frac{1}{2}$
• B. $\frac{2}{3}$
• C. $\frac{1}{4}$
• D. $\frac{1}{5}$

Answer 1

Answer: (B)

$\frac{2}{3}$

According to the problems:

Given that:$A={45}^0$ and $B={30}^0$

This Implies that :

$\frac{\sin A}{\cos A+\sin A\sin B}=\frac{\sin {45}^0}{\cos {45}^0+\sin {45}^0\sin {30}^0}$

This Implies that:

$\frac{\sin A}{\cos A+\sin A\sin B}=\frac{\frac{1}{\sqrt{2}}}{\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}}\times \frac{1}{2}}$

$=\frac{2}{3}$