Question

Prove :
$\frac{\cos (A-B)}{\cos (A+B)}=\frac{\cot A.\cot B+1}{\cot A.\cot B-1}$

Answer 1

Now,

Let $r=\frac{\cos (A-B)}{\cos (A+B)}$

We know that,

$\cos (a+b)=\cos a\cdot \cos b-\sin a\cdot sinb$

$\cos (a-b)=\cos a\cdot \cos b+\sin a\cdot sinb$

$r=\frac{\cos A.\cos B+\sin A.\sin B}{\cos A.\cos B-\sin A.\sin B}$

Dividing both the numerator and the denominator by $\sin A.\sin B$

$r=\frac{\cot A.\cot B+1}{\cot A.\cot B-1}$.

Hence, proved