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Prove that `(Sin a - 2sin^2 A)/(2cos^2 a - Cos A) = Tan A` - CBSE Class 10 - Mathematics

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Question

Prove that `(sin A - 2sin^3 A)/(2cos^3 A - cos A) = tan A`

Solution

Given

`(sin A - 2sin^2 A)/(2cos^2 A - cos A) = tan A`

L.H.S = `(sin A - 2 sin^3 A)/(2 cos^3 A - cos A)`

`= (sin A (1 - 2sin^2 A))/(cos A (2cos^2 A - 1))``

`= tan A ((sin^2 A + cos^2 A - 2sin^2 A))/((2cos^2A - sin^2 A - cos^2 A))`

tan A `(cos^2 A - sin^2 A)/(cos^2 A - sin^2 A)`

= tan A

= R.H.S

Henced proved

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Solution Prove that `(Sin a - 2sin^2 A)/(2cos^2 a - Cos A) = Tan A` Concept: Trigonometric Ratios.
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