Prove the following

Question:

If $\sin \alpha=\frac{1}{2}$ and $\cos \beta=\frac{1}{2}$ then the value of $(\alpha+\beta)$ is

(a) $0^{\circ}$

(b) $30^{\circ}$

(C) $60^{\circ}$

(d) $90^{\circ}$

Solution:

(d) Given, $\sin \alpha=\frac{1}{2}=\sin 30^{\circ}$ $\left[\because \sin 30^{\circ}=\frac{1}{2}\right]$

$\Rightarrow$ $\alpha=30^{\circ}$ 

and $\cos \beta=\frac{1}{2}=\cos 60^{\circ}$ $\left[\because \cos 60^{\circ}=\frac{1}{2}\right]$

$\Rightarrow$ $\beta=60^{\circ}$

$\therefore$ $\alpha+\beta=30^{\circ}+60^{\circ}=90^{\circ}$

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