Question

Prove that (sec θ + tan θ) (1 – sin θ) = cos θ

Answer 1

(sec θ + tan θ) (1 – sin θ) = cos θ

L.H.S. (sec θ + tan θ) (1 – sin θ)

= `(1/cosθ + sinθ/cosθ)(1 - sinθ)`

= `((1 + sinθ)(1 - sinθ))/cosθ`

= `(1 - sin^2θ)/cosθ`

= `(sin^2θ + cos^2θ - sin^2θ)/cosθ`

= `cos^2θ/cosθ`

= cos θ

= R.H.S.

Hence Proved.