Question

Can someone please help me verify each identity, i dont know how

Answer 1

see explanation

Explanation:

using the trigonometric identities

I have used x instead of theta

• sin²x + cos²x = 1

• secx =
`(1)/(cosx)` and tanx =
`(sinx)/(cosx)`

consider the left side

`(sinx)/(cosx)` +
`(cosx)/(1+sinx)`

Combine the fractions

`(sinx(1+sinx)+sos^2x)/(cosx(1+sinx))`

=
`(sinx+sin^2x+cos^2x)/(cosx(1+sinx))`

=
`(1+sinx)/(cosx(1+sinx))`

=
`(1)/(cosx)` = secx = right side → verified