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Prove the following: cos^2 2x - cos^2 6x...

Prove the following: `cos^2 2x - cos^2 6x = sin 4x sin 8x`

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MODERN PUBLICATION-TRIGNOMETRY-EXERCISE
  1. Prove that : sqrt((1-cos frac (5pi)(3))/2) =1/2.

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  2. Prove that : sin^2 6x-sin^2 4x= sin 2x sin 10x.

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  3. Prove the following: cos^2 2x - cos^2 6x = sin 4x sin 8x

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  4. Find sin 7 1^@/2, cos 7 1^@/2 and tan 11 1^@/4.

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  5. Prove that : tan 142 1^@/2 =2+sqrt2-sqrt3-sqrt6.

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  6. If theta be any real, prove that : cos4 theta=1-8 sin^2 theta cos^2 t...

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  7. If theta be any real, prove that : sin5 theta= 5sin theta-20 sin^3 the...

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  8. Prove the following: cot x cot 2x -cot 2x cot 3x -cot 3x cot x = 1

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  9. Prove that: sin 3x + sin 2x -sin x = 4sin x cosfrac(x)(2)cosfrac(3x)(2...

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  10. Prove that: (sin 3x + sin x) sin x + (cos 3x -cos x) cos x = 0

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  11. Prove that cos^2 x + cos^2 (x+ pi/3) + cos^2(x- pi/3) =3/2.

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  12. If cos theta = (cos phi-e)/(1-e cos phi), show that : tan frac (theta)...

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  13. Prove that : sin 36^@ sin 72^@ sin 108^@ sin 144^@ =5/16.

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  14. Prove that sin frac (pi)(10)+ sin frac (13 pi)(10)=-1/2.

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  15. Prove that : sin^2 18^@ +cos^2 36^@= 3/4.

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  16. Prove that : sin^2 24^@ -sin^2 6^@= 1/8 (sqrt5-1).

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  17. Prove that sin 18^@ and cos 36^@ are the roots of the equation : 4x^2-...

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  18. Prove that : sin 12^@ sin48^@ sin 54^@=1/8.

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  19. Prove that : sin 6^@ sin 42^@ sin 66^@ sin 78^@ =1/16.

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  20. Prove that cos 6^(@) cos 42^(@) cos 60^(@) cos 78^(@)=1/16 .

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