Question

Sin(A+B)/sin A cos B
= 1 + cot A tan B
how to verify the identity?

Answer 1

see explanation

Explanation:

Using the identities

sin(A + B) = sinAcosB + cosAsinB

cotA =
`(cosA)/(sinA)` , tanA =
`(sinA)/(cosA)`

Consider the left side

`(sin(A+B))/(sinAcosB)`

=
`(sinAcosB+cosAsinB)/(sinAcosB)`

=
`(sinAcosB)/(sinAcosB)` +
`(cosAsinB)/(sinAcosB)`

= 1 +
`(cosA)/(sinA)` .
`(sinB)/(cosB)`

= 1 + cotA tanB = right side , thus verified