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If costheta=cosalphacosbeta , prove tha...

If `costheta=cosalphacosbeta` , prove that `t a n(theta+alpha)/2t a n(theta-alpha)/2=t a n^2beta/2` .

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RD SHARMA ENGLISH-TRIGONOMETRIC RATIOS OF MULTIPLE AND SUBMULTIPLE ANGLES-All Questions
  1. Prove that: t a nalpha+2tan2alpha+4tan4alpha+8cot8alpha=cotalpha

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  18. Prove that: (1+sin2theta+cos2theta)/(1+sin2theta-cos2theta)=cot theta

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  19. Prove that: (1+sintheta-costheta)/(1+sintheta+costheta)=tan(theta/2)

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  20. Prove that: (costheta)/(1+sintheta)=tan(pi/4-theta/2)

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