Question

How do you verify `(-1) / (tanx - secx) = (1 + sinx) / (cosx)`?

Answer 1

Verify trig expression.

Explanation:

Develop the left side.

`- 1/((sin x)/(cos x) - 1/(cos x)) = - ((cos x)/(sin x - 1)) = (cos x)/(1 - sin x)`

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