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Prove the following : (sinx +sin3x)/(c...

Prove the following :
`(sinx +sin3x)/(cos x + cos 3x)= tan 2x`.

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MODERN PUBLICATION-TRIGNOMETRY-EXERCISE
  1. Prove the following : (sin 5x + sin3x)/(cos 5x + cos 3x)= tan 4x.

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  2. Prove the following : (sinx +siny)/(cos x+cos y)= tan frac (x+y)(2).

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  3. Prove the following : (sinx +sin3x)/(cos x + cos 3x)= tan 2x.

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  4. Prove the following: (sin x-sin y)/(cosx + cos y)=tanfrac(x-y)(2)

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  5. Prove the following : (cos 7x + cos 5x)/(sin 7x-sin 5x) =cot x.

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

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

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  8. Prove the following : 4 sin A sin (60^@ + A) sin (60^@ - A) = sin 3A...

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  9. Prove the following : sin 10^@ + sin 20^@ + sin 40^@ + sin 50^@ = si...

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  10. Prove the following : sin 51^@ + cos 81^@ = cos 21^@.

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  11. Prove the following : sin 10^@ sin 50^@ sin 70^@ = 1/8.

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  12. Prove the following : sin 10^@ sin 30^@ sin 50^@ sin 70^@ = 1/16.

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  13. Prove the following : sin 20^@ sin 40^@ sin 60^@ sin 80^@ = 3/16.

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  14. Prove the following : cos 10^@ cos 50^@ cos 70^@ = sqrt3/8.

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

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  16. Prove the following : cos 20^@ cos 40^@ cos 80^@ =1/8.

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

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

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

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

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