Question

Prove that
cot A + cot B=
2 sin(A + B)/COS (A – B) –COS(A + B)​

Answer 1

Answer:

Given ⇒cotAcotB=2

So, cosAcosB=2sinAsinB        ...(1)

Given cos(A+B)=53 

So, cosAcosB−sinAsinB=53      ....(2)

From eq.(1) and eq.(2)

sinAsinB=53

Answer 2

cosA/SinA + CosB/SiB

= CosASinB+SinBCosA/(SinASinB)

=2Sin(A+B)/2(Cos(A-B)-Cos(A+B))

=R.H.S