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Prove that sin A sin(60° - A) sin(60° + ...

Prove that `sin A sin(60° - A) sin(60° + A) = 1/4 sin3A`

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MODERN PUBLICATION-TRIGNOMETRY-EXERCISE
  1. If 2costheta=x+1/x, prove that 2cos3theta=x^3+1/x^3

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  2. Prove that : 2 cos theta= sqrt (2+ sqrt(2+2 cos 4 theta)).

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  3. Prove that sin A sin(60° - A) sin(60° + A) = 1/4 sin3A

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  4. Prove that : tan A+tan (60^@+A)-tan (60^@-A)=3 tan 3A.

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  5. Prove that : cos^2 A+cos^2 (A+120^@)+ cos^2 (A-120^@)=3/2.

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  6. If tan^2 theta=2 tan^2 phi+1, show that cos 2 theta+ sin^2 phi=0.

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  7. Find sinfrac(x)(2), cosfrac(x)(2) and tanfrac(x)(2) in the following:-...

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  8. Find sinfrac(x)(2), cosfrac(x)(2) and tanfrac(x)(2) in the following:-...

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  9. Find sinfrac(x)(2), cosfrac(x)(2) and tanfrac(x)(2) in the following:-...

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  10. If tan frac (x)(2)= m/n, prove than m sin x+n cos x=n.

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  11. If tan theta =a/b, prove that a sin 2 theta+b cos 2 theta=b.

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  12. Prove that (cos^3 theta -cos 3 theta)/(cos theta)+ (sin^3 theta+sin3 t...

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  13. Evaluate : sin frac (3 pi)(8).

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  14. Evaluate : sin frac (5 pi)(24).

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  15. Evaluate : tan frac (pi)(8).

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  16. Prove that : sin^4 frac (pi)(8)+ sin^4 frac (3pi)(8)+sin^4 frac (5pi)...

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  17. Prove that : sqrt((1-cos frac (5pi)(3))/2) =1/2.

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

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

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

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