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

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

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RD SHARMA ENGLISH-TRIGONOMETRIC RATIOS OF MULTIPLE AND SUBMULTIPLE ANGLES-All Questions
  1. Prove that :cos^3 2theta+3cos2theta=4(cos^6theta-sin^6 theta)

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

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

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

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

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

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

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

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

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

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

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

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

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

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  15. If costheta=4/5a n d\ theta is acute, find the t a n2theta

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  16. If sintheta=4/5 and 0ltthetaltpi/ 2, find the value of sin4theta

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  17. Prove that: \ cos7^0cos 14^0cos 28^0cos 56^0=(sin 68^0)/(16cos83^0)

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  18. Prove that: cos(pi/5)cos((2pi)/5)cos((4pi)/5)cos((8pi)/5)=(-1)/16

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  19. cos(pi/65)cos((2pi)/65)cos((4pi)/65)cos((8pi)/65)cos((16pi)/65)cos((32...

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  20. If 2\ t a nalpha=3t a nbeta, prove that tan(alpha-beta)=(sin2beta)/(5...

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