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Prove that: (costheta)/(1+sintheta)=tan(...

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

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RD SHARMA ENGLISH-TRIGONOMETRIC RATIOS OF MULTIPLE AND SUBMULTIPLE ANGLES-All Questions
  1. Prove that :(sintheta +sin2theta)/(1+costheta+cos2theta)=tantheta

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

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

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

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

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

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

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

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

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

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

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

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  13. Prove that: tan(pi/4+theta)+tan(pi/4-theta)=2sec2theta .

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  14. Prove that: cot^2A-tan^2A=4\ cot2A cos e c2A

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  15. sin4A=4sinAcos^3A-4cosAsin^3A

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  16. Prove that: \ sin3x+sin2x-sin x=4sin xcos(x/2)cos((3x)/2)

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  17. If cos x=\ -3/5a n d\ x lies in the IIIrd quadrant, find the values of...

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  18. If cos x=-3/5a n d\ x lies in IInd quadrant, find the values of sin2x\...

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  19. If sinx=(sqrt(5))/3a n d\ x lies in IInd quadrant, find the values of ...

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

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