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sinalpha+sinbeta=a ,cosalpha+cosbeta=b=>...

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

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`sin a+sin beta=a `
` Rightarrow 2 sin frac{a+beta}{2} cdot cos frac{a-beta}{2}=a`
` cos a+cos beta=b Rightarrow 2 cos frac{a+beta}{2} cdot cos frac{a-beta}{2}=b`
Dividing (1) and (2), we get
`tan frac{a+beta}{2}=frac{a}{b}`
` ...
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RD SHARMA-TRIGONOMETRIC RATIOS OF MULTIPLE AND SUBMULTIPLE ANGLES-Solved Examples And Exercises
  1. cos(pi/15)cos((2pi)/15)cos((3pi)/15)cos((4pi)/15)cos((5pi)/15)cos((6pi...

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

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

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

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

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

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

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  8. (1+sin2theta-cos2theta)/(1+sin2theta+cos2theta)=tantheta

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  9. (sintheta +sin2theta)/(1+costheta+cos2theta)=tantheta

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

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

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

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  13. Prove that: (cosalpha+cosbeta)^2+(s inalpha+s inbeta)^2=4cos^2\ \ ((al...

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  14. Prove that: 1+cos^2 2x=2(cos^4x+sin^4x)

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  15. cos^3 2theta+3cos2theta=4(cos^6theta-sin^6 theta)

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

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  17. Prove that:cos^2(pi/4-theta)-sin^2(pi/4-theta)=s in2theta

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

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

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  20. cos^6A-sin^6A=cos2A(1-1/4sin^2 2A)

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