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Prove that: 2cos frac (pi)(13)cos frac (...

Prove that: `2cos frac (pi)(13)cos frac (9pi)(13)+cos frac (3pi)(13)+cos frac (5pi)(13)=0`

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

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

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

Prove that: 2sin^2frac (pi)(6)+cosec^2frac (7pi)(6)cos^2frac (pi)(3)=3/2

The value of : (1+cos frac (pi)(6)) (1+cos frac (pi)(3))(1+cos frac (2pi)(3)) (1+cos frac (7pi)(6)) is:

In any triangle ABC, prove that : cos frac (A)(2) +cos frac (B)(2)+cos frac (C)(2)= 4 cos frac (pi-A)(4) cos frac (pi-B)(4) cos frac (pi-C)(4) .

Prove that: 2sin^2frac (3pi)(4)+2cos^2frac(pi)(4)+2sec^2frac (pi)(3)=10

MODERN PUBLICATION-TRIGNOMETRY-EXERCISE
  1. Prove the following : tan 20^@ tan 40^@ tan 60^@ tan 80^@=3.

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  2. Prove the following : tan 20^@ tan 40^@ tan 80^@= tan 60^@.

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  3. Prove that: 2cos frac (pi)(13)cos frac (9pi)(13)+cos frac (3pi)(13)+co...

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  4. Prove the following : sin alpha+ sin beta+ sin gamma - sin (alpha+be...

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  5. Prove the following : cot 4 theta(sin 5 theta+ sin 3 theta)=cot thet...

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  6. Prove the following : cos 3 theta+ cos 5 theta+ cos 7 theta+ cos 9 t...

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  7. Prove the following: sin2 x + 2 sin 4x + sin 6x = 4 cos^2 x sin 4x

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  8. Prove the following : sin theta+ sin 3 theta+ sin 5 theta+sin 7 thet...

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  9. Prove the following : cos 7 theta + cos 5 theta + cos 3 theta +cos t...

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  10. Prove the following : sin alpha+ sin (alpha+ (2 pi)/3)+ sin (alpha+ ...

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  11. Prove the following : cos A + cos (120^@ - A) + cos (120^@+ A) = 0.

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  12. Prove the following : (sin11 A sin A +sin 7A sin 3A)/ (cos11A sin A ...

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  13. Prove the following: (cos4x + cos3x + cos2x)/(sin4x + sin 3x + sin 2x)...

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  14. Prove the following : (sin 5x -2sin 3x+sinx)/(cos 5x-cos x)= tan x.

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  15. Prove that: ((sin 7x + sin 5x) + (sin 9x + sin 3x))/((cos7x + cos5x) +...

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  16. Prove the following: (sin x -sin 3x)/(sin^2 x -cos^2 x)= 2sinx

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  17. Prove that: (cos x + cos y)^2 + (sin x -sin y)^2 = 4 cos^2frac (x+y)(2...

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  18. Prove that: (cosx-cosy)^2 +(sinx-siny)^2=4 sin^2frac (x-y)(2)

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  19. Prove the following: cot 4x (sin 5x + sin 3x) = cot x (sin 5x -sin 3x)

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  20. If alpha+beta=pi/2, then the maximum value of cosalpha cos beta is:

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