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Question
Prove that: `1/(sec θ - tan θ) = sec θ + tan θ`.
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Solution
LHS = `1/(sec θ - tan θ)`
= `1/((1/cos θ) - (sin θ/cos θ))`
= `(cos θ xx (1 + sin θ))/((1 - sin θ) xx ( 1 + sin θ))`
= `(cos θ( 1 + sin θ))/(1 - sin^2 θ)`
= `(cos θ( 1 + sin θ))/(cos^2 θ)`
= `1/cos θ + sin θ/cos θ`
= sec θ + tan θ
= RHS
Hence proved.
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