Prove the identity sinabsinabcosabcosabtanbSolutionsinabsina

Prove the identity: (sin(a+b)-sin(a-b))/(cos(a+b)+cos(a-b))=tan(b)

Solution

(sin(a+b)-sin(a-b))/(cos(a+b)+cos(a-b))

We have to use the following formula

sinA - sinB=2cos(A+B)/2 sin (A-B)/2

cos A + cos B= 2cos(A+B)/2 cos(A-B)/2

2cosb sina/2cos a cos b= sin b/cos b = tan b