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(sinA+sin3A)/(cosA+cos3A)=tan2A...

`(sinA+sin3A)/(cosA+cos3A)=tan2A`

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`LHS:`

`frac{sin A+sin 3 A}{cos A+cos 3 A}`

`Rightarrow frac{2 sin (frac{3 A+A}{2}) cos (frac{3 A-A}{2})}{2 cos (frac{3 A+A}{2}) cos (frac{3 A-A}{2})}`

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(sin A+sin3A)/(cos A+cos3A)=tan2A

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RD SHARMA-TRANSFORMATION FORMULAE-Solved Examples And Exercises
  1. Prove that: (sin 5A-sin 3A)/(cos5A+cos3A)=t a n A

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  2. Prove that: (sin A+sin B)/(cos A+cos B)=tan((A+B)/2)

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  3. (sinA+sin3A)/(cosA+cos3A)=tan2A

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  4. Prove that: (cos7A+cos5A)/(sin7A-sin5A)=cot A

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  5. Prove that: (cos9x-cos5x)/(sin 17 x-sin3x)=\ -(sin2x)/(cos 10 x)

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  6. Prove that: (sin5x+sin3x)/(cos5x+cos3x)=t a n4x

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  7. Prove that cot4x(sin5x+sin3x)=cot x(sin5x-sin3x)

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  8. Prove that : sin x+sin3x+sin5x+sin7x=4cos x\ cos2xsin4x

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  9. Prove that:\ (sin3A+sin A)sin A+(cos3A-cos A)cos A=0

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  10. show that cos2thetacos(theta/2)-cos3thetacos(9theta/2)=sin5thetasin(5t...

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  11. Prove that: (cosalpha+cosbeta)^2+(sinalpha+sinbeta)^2=4cos^2((alpha-be...

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  12. Prove that: (cosalpha-cosbeta)^2+(sinalpha-sinbeta)^2=4sin^2((alpha-be...

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  13. Prove that: cosalpha+cosbeta+cosgamma+cos(alpha+beta+gamma)=4cos(alp...

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  14. Prove that: (cos4x+cos3x+cos2x)/(sin4x+sin3x+sin2x)=cot3x

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  15. Prove that: (cos2A\ cos3A-cos2Acos7A+cos10 A cos A)/(sin4A\ sin3A-sin2...

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  16. If three angles A, B, and C are in A.P. prove that: cot B=(sin A-sin C...

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  17. Prove that: (cos6theta+6cos4theta+15 cos2theta+10)/(cos5theta+5cos3the...

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  18. Express each of the following as the product of sines and cosines: sin...

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  19. Express each of the following as the product of sines and cosines: cos...

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  20. Express each of the following as the product of sines and cosines: sin...

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