Question

Prove that
$\sin {38}^o+\sin {22}^o=\sin {82}^o$

Answer 1

$\sin {38}^o+\sin {22}^o=\sin {82}^o$

$L.H.S=\sin {38}^o+\sin {22}^o$

$=2\sin \left(\frac{{38}^o+{22}^o}{2}\right)\cos \left(\frac{{38}^o-{22}^o}{2}\right)$ $[\because \sin A+\sin B=2\sin \left(\frac{A+B}{2}\right)\cos \left(\frac{A-B}{2}\right)]$

$=2\sin {30}^o.\cos 8^o$

$=2\times \frac{1}{2}.\cos ({90}^o-8^o)$ $[\because \sin {30}^o=\frac{1}{2}]$

$=\sin {82}^o$

$=R.H.S$

$\therefore$ $\sin {38}^o+\sin {22}^o=\sin {82}^o$ ---- [ Proved ]