Question

If A, B, C are the angles of a $\Delta$ such that tan B tan C = p and A = $\frac{\pi }{4}$ ,then cos (B - C) =

• A. $\frac{\sqrt{2}(1+p)}{(p-1)}$
• B. $\frac{1+p}{p-1}$
• C. $\frac{1+p}{\sqrt{2}(p-1)}$
• D. None of these

Answer 1

The correct option is C $\frac{1+p}{\sqrt{2}(p-1)}$

$B+C=\frac{3\pi }{4}$ and $\tan B\tan C$ $=p\Rightarrow \frac{\sin B\sin C}{\cos B\cos C}$ =$\frac{p}{1}$
$\Rightarrow \frac{\cos (B-C)}{\cos (B+C)}=\frac{1+p}{1-p}\Rightarrow \cos (B-C)=\frac{1+p}{1-p}.\cos \frac{3\pi }{4}=\frac{1+p}{\sqrt{2}(p-1)}$