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Prove the following : tan 20^@ tan 40^...

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

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MODERN PUBLICATION-TRIGNOMETRY-EXERCISE
  1. Prove the following : cos 10^@ cos 30^@ cos 50^@ cos 70^@ = 3/16.

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  2. Prove the following : tan 20^@ tan 40^@ tan 60^@ tan 80^@=3.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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