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

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

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`cos5A = cos(3A+2A) = cos3Acos2A - sin3Asin2A`
`=(4cos^3A-3cosA)(2cos^2A -1) - (3sinA - 4sin^3A)(2sinAcosA)`
`=(8cos^5A-10cos^3A+3cosA)- (3-4sin^2A)(2sin^2AcosA)`
`=(8cos^5A-10cos^3A+3cosA)- (3-4(1-cos^2A))(2(1-cos^2A)cosA)`
`=(8cos^5A-10cos^3A+3cosA)- (3-4+4cos^2A)(2cosA - 2cos^3A)`
`=(8cos^5A-10cos^3A+3cosA)- (-8cos^5A+10cos^3A- 2cosA)`
`=16cos^5A-20cos^3A+5cosA= 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-cosalpha.cosbeta) , prove that t a ...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  20. Prove that : cos 20^0cos 40^0cos 60^0cos 80^0=1/(16)

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