Given that sin$\alpha$ = $\frac{1}{2}$ and cos$\beta$ = $\frac{1}{2}$, then the value of ($\alpha$ + $\beta$) is ______.

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KollegeApply · Accepted Answer

Given that sin$\alpha$ = $\frac{1}{2}$ and cos$\beta$ = $\frac{1}{2}$, then the value of ($\alpha$ + $\beta$) is $90^\circ$. Explanation: Given, sin$\alpha$ = $\frac{1}{2}$ = sin$30^\circ$ ...[∵ sin 30^circ = $\frac{1}{2}$] $\Rightarrow$ $\alpha$ = $30^\circ$ And cos$\beta$ = $\frac{1}{2}$ = cos$60^\circ$ ...[∵ 60^circ = $\frac{1}{2}$] $\Rightarrow$ $\beta$ = $60^\circ$ $\therefore$ $\alpha$ + $\beta$ = $30^\circ$ + $60^\circ$ = $90^\circ$

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