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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. sin(pi/18)*sin(5pi/18)*sin(7pi/18)

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  2. Prove:cos(pi/15)cos((2pi)/15)cos((3pi)/15)cos((4pi)/15)cos((5pi)/15)co...

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

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

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  5. Prove that sqrt((1-cos2theta)/(1+cos2theta))=tantheta where tantheta>0

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  6. Prove that: (sin2theta)/(1-cos2theta)=cottheta

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

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  8. Prove that: \ sqrt(2+sqrt(2+2cos4theta))=2costheta

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  9. Prove :(1+sin2theta-cos2theta)/(1+sin2theta+cos2theta)=tantheta

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  10. Prove that :(sintheta +sin2theta)/(1+costheta+cos2theta)=tantheta

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

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

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  13. Prove that: sin^2(pi/8)+sin^2((3pi)/8)+sin^2((5pi)/8)+sin^2((7pi)/8)=2

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  14. Prove that: (cosalpha+cosbeta)^2+(sinalpha+sinbeta)^2=4cos^2\ \ ((alph...

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  15. Prove that: 1+cos^2 2theta=2(cos^4theta+sin^4theta)

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  16. Prove that :cos^3 2theta+3cos2theta=4(cos^6theta-sin^6 theta)

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  17. Prove that : (sin3A+sin A)sin A+(cos3A-cos A)cos A=0

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  18. Prove that:cos^2(pi/4-theta)-sin^2(pi/4-theta)=sin2theta

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  19. Prove that: cos4A=1-8cos^2\ A+8cos^4\ A

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  20. Prove that 3(sinx-cosx)^4+4(sin^6x+cos^6x)+6(sinx+cosx)^2=13

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