Question

IF $\alpha$ and $\beta$ are angles in the first quadrant $\tan \alpha =\frac{1}{7}.\sin \beta =\frac{1}{\sqrt{10}}$ , then the value of $\alpha +2\beta$ is

• A. $0^{\circ }$
• B. ${30}^{\circ }$
• C. ${45}^{\circ }$
• D. ${60}^{\circ }$

Answer 1

The correct option is C ${45}^{\circ }$

We have,

$\tan \alpha =1/7$

$\alpha ={\tan }^{-1}1/7$

$\alpha =8.13$

$\sin \beta =\frac{1}{\sqrt{10}}$

$\beta ={\sin }^1\frac{1}{\sqrt{10}}$

$\beta =18.43$

Question given $\alpha +2\beta$............(1)

$\alpha$ and $\beta$ value put in this equation(1)

$=8.13+2\left(18.43\right)$

$=8.13+36.86$

$={45}^0$

Hence this is the answer