Question

Evaluate the following: `((1 - cosθ)(1 + cosθ))/((1 - sinθ)(1 + sinθ)` if θ = 30°

Answer 1

θ = 30°

`((1 - cosθ)(1 + cosθ))/((1 - sinθ)(1 + sinθ)`

= `(1 - cos^2θ)/(1 - sin^2 θ)`

= `(1 - cos^2 30°)/(1 - sin^2 30°)`

= `(1 - (sqrt(3)/2)^2)/(1 - (1/2)^2`

= `( 1 - 3/4)/(1 - 1/4)`

= `(1/4)/(3/4)`

= `(1)/(3)`.