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If 2\ t a nalpha=3t a nbeta, prove that...

If `2\ t a nalpha=3t a nbeta,` prove that `tan(alpha-beta)=(sin2beta)/(5-cos2beta)`

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RD SHARMA ENGLISH-TRIGONOMETRIC RATIOS OF MULTIPLE AND SUBMULTIPLE ANGLES-All Questions
  1. Prove that: cos(pi/5)cos((2pi)/5)cos((4pi)/5)cos((8pi)/5)=(-1)/16

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

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

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

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

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

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

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

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

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

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  11. Prove that cos6A=32cos^6A-48cos^4A+18cos^2A-1

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  12. Prove that : cos Acos(60-A)cos(60+A)=1/4cos3A

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  13. Prove that: "s i n A s i n"(60-"A")sin(60+"A")=1/4sin3"A"dot

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  14. Prove that: "sin"20^0"sin"40^0"sin"60^0"sin"80^0=3/(16)

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  15. prove sin(5theta) = 16sin^5(theta)-20sin^3(theta)+5sin(theta)

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  16. Prove that 4(cos ^(3) 10^(@) + sin ^(3) 20^(@)) = 3 ( cos 10^(@) + sin...

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  17. Prove the following identity: cos^3thetasin3theta+sin^3thetacos3theta=...

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  18. Prove the following identity: \ t a nthetat a n(theta+60^0)+t a ntheta...

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  19. Prove that: t a nA+tan(60^0+A)-t a n(60^0-A)=3t a n3A

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  20. Prove that: cotA+"cot"(60^0+A)-cot(60^0-A)=3cot3A

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