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Prove that:sin2x+2sin4x+sin6x=4cos^2xsin...

Prove that:`sin2x+2sin4x+sin6x=4cos^2xsin4`

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`LHS=sin2x+2sin4x+sin6x`
`=[sin2x+sin6x]+2sin4x`
`=[2sin((2x+6x)/2)cos((2x-6x)/2)]+2sin4x`
`=2sin4xcos2x+2sin4x`
`=2sin4x(cos2x+1)`
`=2sin4x xx 2 cos^2x`
`=4cos^2x sin4x`
`=RHS`
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NCERT ENGLISH-TRIGONOMETRIC FUNCTIONS-All Questions
  1. Prove that: sin^2 6x-sin^2 4x=sin2xsin10 x

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  2. Prove that:cos^2 2x-cos^2 6x=sin4xsin8x

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  3. Prove that:sin2x+2sin4x+sin6x=4cos^2xsin4

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  4. Prove that:cot 4x (sin 5x + sin 3x) = cot x (sin 5x - sin 3x)

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  5. Prove that:(cos9x-cos5x)/(sin17 x-sin3x)=-(sin2x)/(cos10 x)

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  6. Prove that:(sin5x+sin3x)/(cos5x+cos3x)=tan4x

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  7. Prove that:(sinx-siny)/(cosx+cosy)=tan(x-y)/2

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  8. Prove that:(sinx+sin3x)/(cosx+cos3x)=tan2x

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  9. Find the values of the trigonometric function tan (19pi)/3

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  10. Find the values of the trigonometric function sin (-(11pi)/3)

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  11. Find the value of other five trigonometric function cosx=-1/2, x lies...

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  12. Find the value of other five trigonometric function sinx=3/5, x lies ...

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  13. Find the value of other five trigonometric function cotx=3/4, x lies ...

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  14. Find the value of other five trigonometric function secx=(13)/5, x li...

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  15. Find the value of other five trigonometric function tanx=-5/(12), x l...

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  16. Find the values of the trigonometric function sin 765^(@)

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  17. Find the values of the trigonometric function c o s e c(-1410^@).

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  18. cot^2pi/6+cose c(5pi)/6+3tan^2pi/6=6

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  19. 2sin^2(pi/6 )+c o s e c^2((7pi)/6)cos^2(pi/3)=3/2

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  20. sin^2pi/6+cos^2pi/3-tan^2pi/4=-1/2

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