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If `sin(theta+alpha)=a, a n dsin(theta+beta)=b ,` prove that `cos2(alpha-beta)-4a bcos(alpha-beta)=1-2a^2-2b^2`

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RD SHARMA ENGLISH-TRIGONOMETRIC RATIOS OF MULTIPLE AND SUBMULTIPLE ANGLES-All Questions
  1. If tanalpha=1/7,sinbeta=1/(sqrt(10)), prove thatalpha+2beta=pi/4 , whe...

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  2. If tan(pi/4+theta/2)=tan^3(pi/4+alpha/2) then sin(theta)=(sin(alpha)(...

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  3. If sin(theta+alpha)=a, a n dsin(theta+beta)=b , prove that cos2(alpha-...

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  4. Prove that: t a nalpha+2tan2alpha+4tan4alpha+8cot8alpha=cotalpha

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  5. If t a nalpha=p/q , where alpha=6beta,alpha being acute angle, prove...

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  6. If costheta=cosalphacosbeta , prove that t a n(theta+alpha)/2t a n(th...

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  7. If t a ntheta/2=sqrt((a-b)/(a+b))tanvarphi/2 , prove that costheta=(a ...

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  8. Prove that: (2cos2^ntheta+1)/(2costheta+1)=(2costheta-1)(2cos2theta-1)...

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  9. If t a ntheta/2=sqrt((a-b)/(a+b))tanvarphi/2 , prove that costheta=(a ...

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  10. Prove that: sin3e sin^3e+cos3ecos^3e=cos^3 2e

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  11. If cosalpha+cosbeta+cosgamma=0 , then prove that cos3alpha+cos3beta+co...

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  12. If costheta=(cosalpha cosbeta)/(1-sinalphasinbeta) , prove that one va...

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  13. If costheta=(cosalpha-cosbeta)/(1-cosalpha.cosbeta) , prove that t a ...

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  14. sin5A=5cos^4AsinA-10cos^2Asin^3A+sin^5A

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  15. Prove that: cos5A=16cos^5A-20cos^3A+5cosA

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  16. Prove that: sin18^0=(sqrt(5)-1)/4 .

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  17. Prove that: |sintheta."sin"(60-theta).sin(60+theta)|lt=1/4 for all val...

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

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  19. Prove that sin(2theta)/(1-cos2theta)=cot theta

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  20. Prove that: (cos2theta)/(1+sin2theta)=tan(pi/4-theta)

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