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Question
Prove that `sqrt((1 - sin θ)/(1 + sin θ)) = sec θ - tan θ`.
Solution
L.H.S. = `sqrt(((1 - sin θ)(1 - sin θ))/((1 + sin θ)(1 - sin θ)))`
= `sqrt((1 + sin^2θ - 2sinθ)/(1 - sin^2θ)`
= `sqrt((1 + sin^2θ - 2sinθ)/(cos^2θ)`
= `sqrt( 1/cos^2θ + sin^2θ/cos^2θ - (2sin θ)/cos θ xx 1/cosθ`
= `sqrt( sec^2θ + tan^2 θ - 2 tan θ. sec θ)`
= `sqrt((sec θ - tan θ)^2)`
= sec θ - tan θ
= R.H.S.
Hence proved.
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Activity:
L.H.S = `square`
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