Question

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

Answer 1

Given: sinA = cosB

$$\begin{gathered} \sin A=\cos B \\ \Rightarrow \cos \left(90°-A\right)=\cos B\left(\because \sin \theta =\cos \left(90°-\theta \right)\right) \\ \Rightarrow 90°-A=B \\ \Rightarrow 90°=B+A \\ \Rightarrow A+B=90° \\ \mathrm{Hence},\mathrm{the}\mathrm{correct}\mathrm{option}\mathrm{is}\left(\mathrm{d}\right). \end{gathered}$$