Question

If A and B are acute angles such that sin A = cos B, then (A + B) = ?
(a) 45°
(b) 60°
(c) 90°
(d) 180°

Answer 1

$$\begin{gathered} \text{(c) 90°} \\ \text{We have:} \\ \text{sinA=cosB} \\ =>\text{cos}({90}^0-\text{A})=\text{cos B}[\because \text{B and}\text{A}\text{are acute}] \\ =>{90}^0-\text{A}=\text{B} \\ =>{\text{A+B=90}}^0 \\ \therefore {\text{A+B=90}}^0 \end{gathered}$$