Question

If cot A . cot B = 2, then what is the value of cos(A + B) . sec(A - B) ?

• A. 1/3
• B. 2/3
• C. 1
• D. -1

Answer 1

Answer: (A)

1/3

Given $\cot A\cot B=2$

$\Rightarrow \frac{\cos A}{\sin A}.\frac{\cos B}{\sin B}=2\Rightarrow \cos AcosB=2\sin A\sin B\Rightarrow \cos (A-B)=\cos A\cos B+\sin A\sin B=3\sin A\sin B\Rightarrow \cos (A+B)=\cos A\cos B-\sin A\sin B=\sin A\sin B$

Now $\cos (A+B).\sec (A-B)=\frac{\cos (A+B)}{\cos (A-B)}=\frac{\sin A\sin B}{3\sin A\sin B}=\frac{1}{3}$