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

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

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Given, `cos^6A−sin^6A`
`=(cos^2A)^3−(sin^2A)^3`
`=[cos^2A−sin^2A][cos^4A+cos^2Asin^2A+sin^4A]`
...
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  • TRIGONOMETRIC RATIOS OF COMPOUND ANGLES

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RD SHARMA-TRIGONOMETRIC RATIOS OF MULTIPLE AND SUBMULTIPLE ANGLES-Solved Examples And Exercises
  1. Prove that: cos4A=1-8cos^2A+8cos^4 A

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

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

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

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  5. Prove that: cot^2A-tan^2A=4 cot2A cosec2A

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

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  7. Prove that: \ s in3x+s in2x-s in x=4s in xcosx/2cos(3x)/2

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

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

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

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

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  12. If costheta=4/5 and theta is acute, find the tan2theta

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  13. If sinx=4/5 and 0ltxltpi/ 2, find the value of sin4x

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

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

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  16. cos((2pi)/65)cos((4pi)/65)cos((8pi)/65)cos((16pi)/65)=1/16

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

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

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

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  20. If costheta=(cosalpha+cosbeta)/(1+cosalphacosbeta),\ prove that tanth...

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