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

Prove that :
`sin^4 frac (pi)(8)+ sin^4 frac (3pi)(8)+sin^4 frac (5pi)(8)+sin^4 frac (7pi)(8)=3/2`.

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Prove that : sin^2 frac (pi)(8)+ sin^2 frac (3pi)(8)+ sin^2 frac (5pi)(8)+sin^2 frac (7pi)(8)=2 .

Prove that sin frac (pi)(14) sin frac (3 pi)(14) sin frac (5pi)(14) sin frac (7pi)(14)=1/8 .

Prove that : sin frac (pi)(5) sin frac (2pi)(5) sin frac (3pi)(5) sin frac (4pi)(5) =5/16 .

Prove that : cos^2 frac (pi)(8)+ cos^2 frac (3 pi)(8)+ cos^2 frac (5 pi)(8) + cos^2 frac (7 pi)(8) =2 .

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

Prove that : 3 sin frac (pi)(6) sec frac (pi)(3)-4 sin frac (5pi)(6) cot frac(pi)(4)=1 .

Prove that : (1+cos frac (pi)(8)) (1+cos frac (3pi)(8)) (1+cos frac (5pi)(8)) (1+cos frac (7pi)(8))=1/8 .

Prove that : sin^2 frac (pi)(6)+ cos^2 frac(pi)(3)- tan^2 frac(pi)(4)=-1/2 .

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

Prove that: sin^2frac (pi)(6)+cos^2frac (pi)(3)-tan^2frac (pi)(4)=-1/2

MODERN PUBLICATION-TRIGNOMETRY-EXERCISE
  1. Evaluate : sin frac (5 pi)(24).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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