Solution :
The formula of cot (A + B) is \(cot A cot B – 1\over cot B + cot A\).
Proof : We have,
cot (A + B) = \(cos (A + B)\over sin(A + B)\)
Using sin (A + B) and cos (A + B) formula,
cot (A + B) = \(cos A cos B – sin A sin B\over sin A cos B + cos A sin B\)
Dividing the numerator and denominator by sin A sin B,
cot (A + B) = \(cot A cot B – 1\over cot B + cot A\)