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If sinalpha+sinbeta=a and cosalpha+cosbe...

If `sinalpha+sinbeta=a` and `cosalpha+cosbeta=b` prove that: `cos(alpha-beta)=((a^2+b^2-2)/2)`

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RD SHARMA ENGLISH-TRIGONOMETRIC RATIOS OF MULTIPLE AND SUBMULTIPLE ANGLES-All Questions
  1. If 2\ t a nalpha=3t a nbeta, prove that tan(alpha-beta)=(sin2beta)/(5...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  19. Prove the following identity: cot A+cot(60^0+A)+cot(120^0+A)=3cot3A

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  20. Prove that: sin^3A+sin^3((2pi)/3+A)+sin^3((4pi)/3+A)=-3/4sin3Adot

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