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Question
Prove the following:
`1/(sinθ + cosθ) + 1/(sinθ - cosθ) = (2 sinθ)/(2sin^2θ - 1)`
Theorem
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Solution
LHS = `((sinθ - cosθ) + (sinθ + cosθ))/((sinθ + cosθ)(sinθ - cosθ))`
= `(2sinθ)/((sinθ + cosθ)(sinθ - cosθ))`
= `(2sinθ)/(sin^2θ = cos^2θ)`
= `(2sinθ)/(sin^2θ - (1 - sin^2θ))`
= `(2sinθ)/(sin^2θ - 1 + sin^2θ)`
= `(2sinθ)/(2sin^2θ - 1)`
LHS = RHS
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