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Prove the following: 1/(sinθ + cosθ) + 1/(sinθ - cosθ) = (2 sinθ)/(2sin^2θ - 1) - Mathematics

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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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Chapter 18: Trigonometric identities - Exercise 18A [Page 423]

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Nootan Mathematics [English] Class 10 ICSE
Chapter 18 Trigonometric identities
Exercise 18A | Q 12. | Page 423
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