Question

If A and B are acute angles and sin A = cos B, show that A + B = 90$°$.

Answer 1

$$\begin{gathered} \mathrm{Given}:\sin \mathrm{A}=\cos \mathrm{B};\mathrm{A}\mathrm{and}\mathrm{B}\mathrm{are}\mathrm{acute}\mathrm{angles} \\ \mathrm{Now},\sin \mathrm{A}=\cos \mathrm{B} \\ \Rightarrow \cos (90°-\mathrm{A})=\cos \mathrm{B}[\because \sin x=\cos (90°-x\left)\right] \\ \Rightarrow (90°-\mathrm{A})=\mathrm{B} \\ \Rightarrow \mathrm{A}+\mathrm{B}=90° \end{gathered}$$

Hence, proved.