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If tan theta =a/b, prove that a sin 2 th...

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

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If theta be any real, prove that : cos4 theta=1-8 sin^2 theta cos^2 theta =1-8 cos^2 theta +8 cos^4 theta .

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MODERN PUBLICATION-TRIGNOMETRY-EXERCISE
  1. Find sinfrac(x)(2), cosfrac(x)(2) and tanfrac(x)(2) in the following:-...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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