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

Prove the following :
`cos 20^@ cos 40^@ cos 60^@ cos 80^@ =1/16`.

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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 : cos 20^@ cos 40^@ cos 80^@ =1/8.

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  3. Prove the following : cos 20^@ cos 40^@ cos 60^@ cos 80^@ =1/16.

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  4. Prove the following : cos 10^@ cos 30^@ cos 50^@ cos 70^@ = 3/16.

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

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

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

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

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

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

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

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

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

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