3. trignometrical ratios,functions and identities — ગણિત ધોરણ 11 સાયન્સ — Question

$A + B + C = \pi \Rightarrow B + C = \pi - A$

$\therefore \cos (B + C) = \cos (\pi - A) \Rightarrow \cos (B + C) = - \cos A$

$ \Rightarrow \cos B\cos C - \sin B\sin C = - \cos B\cos C$

$( \because {\rm{Given}}\cos A = \cos B\cos C)$

$ \Rightarrow 2\cos B\cos C = \sin B\sin C$

$ \Rightarrow \frac{{\cos B\cos C}}{{\sin B\sin C}} = \frac{1}{2}$

$\Rightarrow \cot B\cot C = \frac{1}{2}$.