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Prove that : sin3A+ sin 2A- sinA= 4 si...

Prove that :
`sin3A+ sin 2A- sinA= 4 sinA cos frac (A)(2) cos frac (3A)(2)`.

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If A + B + C =pi , prove that : . sin A + sin B+sinC = 4 cos frac (A)(2) cos frac (B)(2) cos frac (C)(2) .

If A + B + C =pi , prove that : sin A + sin B -sin C = 4 sin frac (A)(2) sin frac (B)(2) cos frac (C)(2) .

If A + B + C =pi , prove that : cos A+cos B - cos C= 4 cos frac (A)(2) cos frac (B)(2) sin frac (C)(2)-1 .

If A + B + C =pi , prove that : cos A - cos B + cos C= -1+4 cos frac (A)(2) sin frac (B)(2) cos frac (C)(2) .

Prove that : sinC +sinD =2 sin frac (C+D)(2) cos frac (C-D) (2) .

If A + B + C =pi , prove that : (sin A + sin B +sin C)/(sin A + sin B -sin C)= cot frac (A)(2) cot frac (B)(2) .

If A+B +C +D= 2 pi , prove that : cos A + cos B + cos C + cos D =-4 cos frac (A+B)(2) cos frac (A+C)(2) cos frac (A+D)(2) .

Prove that : cos C +cosD = 2 cos frac (C+D)(2) cos frac (C-D) (2) .

Prove that : sin 4A=4 sinA cos^3 A- 4 cosA sin^3 A .

Prove that : sinC-sinD = 2 cos frac (C+D)(2) sin frac (C-D) (2) .

MODERN PUBLICATION-TRIGNOMETRY-EXERCISE
  1. Prove the following: cos 4x = 1 - 8sin^2 x cos^2 x

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  2. Prove that : sin 4A=4 sinA cos^3 A- 4 cosA sin^3 A.

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  3. Prove that : sin3A+ sin 2A- sinA= 4 sinA cos frac (A)(2) cos frac (3...

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  4. Prove that (tan^2 theta)/(tan^2 theta-1)+(cosec^2 theta)/ (sec^2 theta...

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  5. If cos theta =1/2(a+1/a), prove that : 2 cos 2 theta= a^2+1/ a^2.

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  6. If cos theta =1/2(a+1/a), prove that : 2 cos 4 theta= a^4+1/ a^4.

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  7. If 2costheta=x+1/x, prove that 2cos3theta=x^3+1/x^3

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

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

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

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

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

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

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

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

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

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

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

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

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

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