Question

Evaluate$\sin 60°\cos 30°+\sin 30°\cos 60°$

Answer 1

Recall the values of required angles from the trigonometry values table

So

$\sin 30°=\frac{1}{2},\cos 30°=\frac{\sqrt{3}}{2},\sin 60°=\frac{\sqrt{3}}{2},\cos 60°=\frac{1}{2}$

Put values in the given expression and simplify by taking LCM

$$\begin{gathered} \Rightarrow \sin 60°\cos 30°+\sin 30°\cos 60° \\ =\frac{\sqrt{3}}{2}\times \frac{\sqrt{3}}{2}+\frac{1}{2}\times \frac{1}{2} \\ =\frac{3}{4}+\frac{1}{4}=\frac{4}{4}=1 \end{gathered}$$
Hence we get $1$ after simplification.