Question

In triangle $ABC$, right-angled at $B$, if $\tan A=\frac{1}{\sqrt{3}}$ find the value of:
(i) $\sin A\cos C+\cos A\sin C$

Answer 1

$\tan A=\frac{1}{\sqrt{3}}A={30}^{o}B=90$

then $C={60}^o$

(i) $\sin A\cos C+\cos A\sin C=\sin (A+C)$

$=\sin {90}^o=1$.