If $\sin{A = \frac{1}{\sqrt{10}}}$ and $\sin{B = \frac{1}{\sqrt{5}}}$, where $A$ and $B$ are positive acute angles, then $A + B$ is equal to

Question

Dr. Abubacker · Accepted Answer

(d)
$\sin{(A + B) = \sin{A\cos{B + \sin{B\cos A}}}}$
$= \frac{1}{\sqrt{10}}.\ \sqrt{1 - \frac{1}{5}} + \frac{1}{\sqrt{5}}\sqrt{1 - \frac{1}{10}}$
$\left\lbrack \because\sin{A = \frac{1}{\sqrt{10}},\sin{B = \frac{1}{\sqrt{5}}}} \right\rbrack$
$= \frac{1}{\sqrt{10}}\sqrt{\frac{4}{5}} + \frac{1}{\sqrt{5}}\sqrt{\frac{9}{10}} = \frac{5}{\sqrt{50}} = \frac{1}{\sqrt{2}} = \sin\frac{\pi}{4}$
$\Rightarrow \ \ A + B = \frac{\pi}{4}$

Q. If $\sin{A = \frac{1}{\sqrt{10}}}$ and $\sin{B = \frac{1}{\sqrt{5}}}$, where $A$ and $B$ are positive acute angles, then $A + B$ is equal to

Explanation

Reviewed by Dr. Abubacker

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