MCQ
Choose the correct answer from the given four options. Given that $\sin\alpha=\frac{1}{2}$ and $\cos\beta=\frac{1}{2}$ then the value of $(\alpha+\beta)$ is :
- A$0^\circ$
- B$30^\circ$
- C$60^\circ$
- ✓$90^\circ$
✓
Answer
Correct option: D.
$90^\circ$
Given $,\sin\alpha=\frac{1}{2}=\sin30^\circ$
$\Big[\because\sin30^\circ=\frac{1}{2}\Big]$
$\Rightarrow\ \alpha=30^\circ$
and $\cos\beta=\frac{1}{2}=\cos60^\circ$
$\Big[\because\cos60^\circ=\frac{1}{2}\Big]$
$\Rightarrow\ \beta=60^\circ$
$\therefore\ \alpha+\beta=30^\circ+60^\circ=90^\circ$
$\Big[\because\sin30^\circ=\frac{1}{2}\Big]$
$\Rightarrow\ \alpha=30^\circ$
and $\cos\beta=\frac{1}{2}=\cos60^\circ$
$\Big[\because\cos60^\circ=\frac{1}{2}\Big]$
$\Rightarrow\ \beta=60^\circ$
$\therefore\ \alpha+\beta=30^\circ+60^\circ=90^\circ$
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