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Prove that: \ sin3x+sin2x-sin x=4sin xco...

Prove that: `\ sin3x+sin2x-sin x=4sin xcos(x/2)cos((3x)/2)`

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RD SHARMA ENGLISH-TRIGONOMETRIC RATIOS OF MULTIPLE AND SUBMULTIPLE ANGLES-All Questions
  1. Prove that: cot^2A-tan^2A=4\ cot2A cos e c2A

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  2. sin4A=4sinAcos^3A-4cosAsin^3A

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  3. Prove that: \ sin3x+sin2x-sin x=4sin xcos(x/2)cos((3x)/2)

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  4. If cos x=\ -3/5a n d\ x lies in the IIIrd quadrant, find the values of...

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  5. If cos x=-3/5a n d\ x lies in IInd quadrant, find the values of sin2x\...

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  6. If sinx=(sqrt(5))/3a n d\ x lies in IInd quadrant, find the values of ...

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  7. Prove that 1+cos^2 2theta=2(cos^4theta+sin^4theta)

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  8. If costheta=4/5a n d\ theta is acute, find the t a n2theta

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  9. If sintheta=4/5 and 0ltthetaltpi/ 2, find the value of sin4theta

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  10. Prove that: \ cos7^0cos 14^0cos 28^0cos 56^0=(sin 68^0)/(16cos83^0)

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  11. Prove that: cos(pi/5)cos((2pi)/5)cos((4pi)/5)cos((8pi)/5)=(-1)/16

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  12. cos(pi/65)cos((2pi)/65)cos((4pi)/65)cos((8pi)/65)cos((16pi)/65)cos((32...

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  13. If 2\ t a nalpha=3t a nbeta, prove that tan(alpha-beta)=(sin2beta)/(5...

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  14. sinalpha+sinbeta=a ,cosalpha+cosbeta=b=>sin(alpha+beta)

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  15. If sinalpha+sinbeta=a and cosalpha+cosbeta=b prove that: cos(alpha-bet...

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  16. If costheta=(cosalpha+cosbeta)/(1+cosalphacosbeta),\ prove that tanth...

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  17. If sec(theta+alpha)+sec(theta-alpha)=2\ s e ctheta, prove that costhet...

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  18. If cos alpha=4/5 and cos beta =5/13, prove that cos (alpha-beta)/2=28/...

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  19. Prove that: 8cos^3pi/9-\ 6cospi/9=1.

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  20. Prove that: 108sinpi/(18)-144sin^3pi/(18)=18

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