Question

$\sin 65°\cos 38°=$

Answer 1

Consider $\sin 65°\cos 38°$

Multiply and divide by $2$

$\frac{1}{2}\left(2\sin 65°\cos 38°\right)$

We know that $2\sin A\cos B=\sin \left(A+B\right)+\sin \left(A-B\right)$

$$\begin{gathered} \therefore \frac{1}{2}\left(2\sin 65°\cos 38°\right)=\frac{1}{2}\left[\sin \left(65°+38°\right)+\sin \left(65°-38°\right)\right] \\ =\frac{1}{2}\left[\sin 103°+\sin 27°\right] \\ but\sin 103°=0.6229 \\ \sin 27°=0.9563 \\ =\frac{1}{2}\left[0.6229+0.9563\right] \\ =\frac{1}{2}\left[1.5292\right] \\ =0.7896 \end{gathered}$$

Hence, $\sin 65°\cos 38°=0.7896$