Question

Prove : Sin (A-B)/Cos (A-B) = Cot A + Cot B/1+
Cot A Cot B ​

Answer 1

Answer:

RHS:

cotA = sinA/cosB

cotB = sinB/cosB

==> (sinA/cosA + sinB/cosB) / (1 + sinA/cosB*sinB/cosB)

= sinAcosB + sinBcosA / cosAcosB + sinAsinB

we know that

sin(A-B) = sinAcosB - cosAsinB

cos(A-B) = cosAcosB + sinAsinB

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

Hence Proved