Question

Complete the identity, sin(a+b)/cosacosb=​

Answer 1

tana + tanb

Explanation:

Using the trigonometric identities

• sin(a + b) = sinacosb + cosasinb

• tanx =
`(sinx)/(cosx)`, then

`(sin(a+b))/(cosacosb)`

=
`(sinacosb+cosasinb)/(cosacosb)`

=
`(sinacosb)/(cosacosb)` +
`(cosasinb)/(cosacosb)`

=
`(sina)/(cosa)` +
`(sinb)/(cosb)`

= tana + tanb