What is the Formula of Cot (A + B) ?

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) = $cot A cot B – 1\over cot B + cot A$