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Express each of the following as the sum...

Express each of the following as the sum or difference of sines and cosines: `\ 2sin4thetasin3theta`

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Express each of the following as the sum or difference of sines and cosines: \ 2cos3thetasin2theta

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RD SHARMA ENGLISH-TRIGONOMETRIC RATIOS OF MULTIPLE AND SUBMULTIPLE ANGLES-All Questions
  1. Prove that: (sin5x-2sin3x+sin x)/(cos5x-cos x)=tanx

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

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

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

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

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

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

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  8. Prove that : cos(pi/7)cos((2pi)/7) cos((3pi)/7)=1/8

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  9. Show that: sin 50^0cos95^0=(sqrt(2)sin35^0-1)/(2sqrt(2))

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  10. Prove that cos((2pi)/(15))cos((4pi)/(15))cos((8pi)/(15))cos((14pi)/(15...

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  11. sin(pi/18)*sin(5pi/18)*sin(7pi/18)

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  12. Prove:cos(pi/15)cos((2pi)/15)cos((3pi)/15)cos((4pi)/15)cos((5pi)/15)co...

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

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

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  15. Prove that sqrt((1-cos2theta)/(1+cos2theta))=tantheta where tantheta>0

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  16. Prove that: (sin2theta)/(1-cos2theta)=cottheta

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

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  18. Prove that: \ sqrt(2+sqrt(2+2cos4theta))=2costheta

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  19. Prove :(1+sin2theta-cos2theta)/(1+sin2theta+cos2theta)=tantheta

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  20. Prove that :(sintheta +sin2theta)/(1+costheta+cos2theta)=tantheta

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