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Question
Prove the following identities:
`1/(sin θ + cos θ) + 1/(sin θ - cos θ) = (2sin θ)/(1 - 2 cos^2 θ)`.
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Solution
LHS = `1/(sin θ + cos θ) + 1/(sin θ - cos θ)`
= `((sin θ - cos θ) + (sin θ + cos θ))/(sin^2 θ - cos^2 θ)`
= `(2 sin θ)/((1 - cos^2 θ) - cos^2 θ)`
= `(2 sin θ)/(1 - 2cos^2 θ)`
= RHS
Hence proved.
RELATED QUESTIONS
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`tan theta + 1/tan theta` = sec θ.cosec θ
Prove that:
`sqrt(sec^2A + cosec^2A) = tanA + cotA`
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`sqrt((1 + cosA)/(1 - cosA)) = cosecA + cotA`
Prove that `sqrt((1 + sin A)/(1 - sin A))` = sec A + tan A.
If A = 60°, B = 30° verify that tan( A - B) = `(tan A - tan B)/(1 + tan A. tan B)`.
Prove that `sin^2 θ/ cos^2 θ + cos^2 θ/sin^2 θ = 1/(sin^2 θ. cos^2 θ) - 2`.
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Prove that `(sintheta + "cosec" theta)/sin theta` = 2 + cot2θ
If sinθ = `11/61`, then find the value of cosθ using the trigonometric identity.
