Question
If in a $$\vartriangle ABC,\frac{a}{{\cos A}} = \frac{b}{{\cos B}},$$ then
A.
$$2\sin A\sin B\sin C = 1$$
B.
$${\sin ^2}A + {\sin ^2}B = {\sin ^2}C$$
C.
$$2\sin A\cos B = \sin C$$
D.
None of these
Answer :
$$2\sin A\cos B = \sin C$$
Solution :
$$\eqalign{
& \frac{{2R\sin A}}{{\cos A}} = \frac{{2R\sin B}}{{\cos B}}\,\,{\text{or, }}\sin A\cos B = \cos A\sin B \cr
& {\text{or, }}2\sin A\cos B = \cos A\sin B + \sin A\cos B = \sin \left( {A + B} \right) = \sin C. \cr} $$