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Prove that sin frac (pi)(10)+ sin frac (...

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

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

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

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

Prove that : sin^2 frac (pi)(6)+ cos^2 frac(pi)(3)- tan^2 frac(pi)(4)=-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 : 2 sin^2 frac (3pi)(4)+ 2cos^2 frac (pi)(4) +2 cos^2 frac (pi)(3)= 5/2 .

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 : 16 cos frac (2pi)(15) cos frac (4pi)(15) cos frac (8pi)(15) cos frac (16pi)(15) =1.

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 .

MODERN PUBLICATION-TRIGNOMETRY-EXERCISE
  1. If cos theta = (cos phi-e)/(1-e cos phi), show that : tan frac (theta)...

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

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

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

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

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

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

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

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

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  10. Prove that : 16 cos frac (2pi)(15) cos frac (4pi)(15) cos frac (8pi)(1...

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  11. Prove that : (1+cos frac (pi)(8)) (1+cos frac (3pi)(8)) (1+cos frac ...

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  12. If A+B+C=pi , then, find sin 2A+ sin 2B+ sin 2C.

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  13. If A+B+C=pi , then, find sin 2A+ sin 2B+ sin 2C.

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

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  15. If A + B + C =pi, prove that : cos 2A - cos 2B + cos 2C= 1-4 sin A co...

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  16. If A + B + C =pi, prove that : cos 2A - cos 2B- cos 2C= -1+4 cos A si...

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

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

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

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

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