If A and B are acute angles such that sin A = cos B then (A + B) = ?


If A and B are acute angles such that sin A = cos B then (A + B) = ?
(a) 30°
(b) 45°
(c) 60°
(d) 90°



Given: sinA = cosB

$\sin A=\cos B$

$\Rightarrow \cos \left(90^{\circ}-A\right)=\cos B \quad\left(\because \sin \theta=\cos \left(90^{\circ}-\theta\right)\right)$

$\Rightarrow 90^{\circ}-A=B$

$\Rightarrow 90^{\circ}=B+A$


$\Rightarrow A+B=90^{\circ}$

Hence, the correct option is $(\mathrm{d})$.



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