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If costheta=(cosalpha+cosbeta)/(1+cosalp...

If `costheta=(cosalpha+cosbeta)/(1+cosalphacosbeta),\ ` prove that `tantheta/2=\ =-tanalpha/2tanbeta/2`

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To prove that \( \tan \frac{\theta}{2} = \pm \tan \frac{\alpha}{2} \tan \frac{\beta}{2} \) given that \[ \cos \theta = \frac{\cos \alpha + \cos \beta}{1 + \cos \alpha \cos \beta}, \] we can follow these steps: ...
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RD SHARMA-TRIGONOMETRIC RATIOS OF MULTIPLE AND SUBMULTIPLE ANGLES-Solved Examples And Exercises
  1. sinalpha+sinbeta=a ,cosalpha+cosbeta=b=>sin(alpha+beta)

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

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

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

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  5. If cos alpha=4/5 and cos beta =5/13, prove that cos (alpha-beta)=56/65

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

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

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  8. Prove that cos6x=32cos^6x-48cos^4x+18cos^2x-1

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

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  10. Prove that: sin A sin(60-A)sin(60+A)=1/4sin3Adot

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

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

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  13. Prove the following identity: 4(cos^3 10^0+sin^3\ \ 20^0)=\ 3\ (cos 10...

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  14. Prove the following identity: cos^3thetas in3theta+sin^3thetacos3theta...

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  15. Prove the following identity: tan θ tan(60^@ +θ)tan(60^@ −θ)=]ta...

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  16. Prove that: t a nA+tan(60^0+A)-t a n(60^0-A)=3t a n3ALet's use the sum...

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

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

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

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  20. Maximum value of |costhetacos(60^0-theta)cos(60^0+theta) for all valu...

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