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