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sin5A=5cos^4AsinA-10cos^2Asin^3A+sin^5A...

`sin5A=5cos^4AsinA-10cos^2Asin^3A+sin^5A`

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`L.H.S. = sin5A = sin(3A+2A) = sin3Acos2A+sin2Acos3A`
`=(3sinA-4sin^3A)(1-2sin^2A)+(4cos^3A-3cosA)(2sinAcosA)`
`=3sinA-6sin^3A-4sin^3A+8sin^5A+8cos^4AsinA - 6sinAcos^2A`
`=sin^5A+5cos^4AsinA-10cos^2Asin^3A = R.H.S.`
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RD SHARMA ENGLISH-TRIGONOMETRIC RATIOS OF MULTIPLE AND SUBMULTIPLE ANGLES-All Questions
  1. If costheta=(cosalpha cosbeta)/(1-sinalphasinbeta) , prove that one va...

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  2. If costheta=(cosalpha-cosbeta)/(1-cosalpha.cosbeta) , prove that t a ...

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  3. sin5A=5cos^4AsinA-10cos^2Asin^3A+sin^5A

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  4. Prove that: cos5A=16cos^5A-20cos^3A+5cosA

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  5. Prove that: sin18^0=(sqrt(5)-1)/4 .

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  6. Prove that: |sintheta."sin"(60-theta).sin(60+theta)|lt=1/4 for all val...

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  7. Prove that: (sin2theta)/(1+cos2theta)=t a ntheta

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  8. Prove that sin(2theta)/(1-cos2theta)=cot theta

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  9. Prove that: (cos2theta)/(1+sin2theta)=tan(pi/4-theta)

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  10. Prove that: (1+sin2theta+cos2theta)/(1+sin2theta-cos2theta)=cot theta

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  11. Prove that: (1+sintheta-costheta)/(1+sintheta+costheta)=tan(theta/2)

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  12. Prove that: (costheta)/(1+sintheta)=tan(pi/4-theta/2)

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  13. Prove that: sin10^0sin30^0sin50^0sin70^0=1/(16)dot

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  14. Prove that : cos4x=1-8sin^2xcos^2x

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  15. Prove that: (sin5x-2sin3x+sin x)/(cos5x-cos x)=tanx

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  16. Prove that : (sinx-sin3x)/(sin^(2)x-cos^(2)x) = 2sinx

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  17. Express each of the following as the sum or difference of sines and ...

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  18. Show that sqrt(3)\ cos e c\ 20^0-sec20^0=4.

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  19. Prove that: tan4theta=(4t a ntheta(1-tan^2theta))/(1-6tan^2theta+tan^4...

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  20. If tanx=3/4, pi < x < (3pi)/2 , find the values of sinx/2, cosx/2 and...

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