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Question
Prove the following identities:
`(sec θ + tan θ)/(sec θ - tan θ) = ((1 + sin θ)/cos θ)^2`
Theorem
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Solution
LHS = `((1/(cos θ) + (sin θ)/(cos θ))/(1/(cos θ) - (sin θ)/(cos θ)))`
= `((1 + sin θ))/((1 - sin θ))`
RHS = `(1 + sin θ)^2/(cos^2θ)`
= `(1 + sin θ)^2/((1 - sin^2θ))`
= `((1 + sin θ))/((1 - sin θ))`
∴ LHS = RHS.
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