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Prove. `(Sina-2sin^3a)/(2cos^3a-cosa)=Tana` - Mathematics

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Prove.
`(sinA-2sin^3A)/(2cos^3A-cosA)=tanA`

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Solution

LHS = `(sinA-2sin^3A)/(2cos^3A-cosA)`

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

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

`=(sinA(cos^2A-sin^2A))/(cosA(cos^2A-sin^2A))`

`=sinA/cosA`

= tan A = RHS

Concept: Trigonometric Identities
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APPEARS IN

Selina Concise Maths Class 10 ICSE
Chapter 21 Trigonometrical Identities
Exercise 21 (A) | Q 34 | Page 325
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