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Prove that 1 + cos 2x + cos 4x + cos 6x ...

Prove that 1 + cos 2x + cos 4x + cos 6x = 4 cos x cos 2x cos 3x

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The correct Answer is:
4 cos x cos 3x . Cos 2x
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Show that (sin 8x cos x - sin 6x cos 3x)/(cos 2x cos x - sin 3x sin 4x) = tan 2x

Prove that (sin 4x + sin 2x)/(cos 4x + cos 2x) = tan 3x .

Prove that (sin x + sin 3x + sin 5x + sin 7x)/(cos x + cos 3x + cos 5x + cos 7x ) = tan 4x

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SURA PUBLICATION-TRIGONOMETRY-EXERCISE 3.6
  1. Express each of the following as a sum or difference. sin 4x cos 2x

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  2. Express each of the following as a sum or difference. 2 sin 10theta c...

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  3. Express each of the following as a sum or difference. cos 5theta cos ...

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  4. Express each of the following as a sum or difference. sin 5 theta sin...

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  5. Express each as a product sin 75^(@) - sin 35^(@)

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  6. Express each as a product cos 65^(@) + cos 15^(@)

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  7. Express each as a product sin 50^(@) + sin 40^(@)

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  8. Express each as a product cos 35^(@) - cos 75^(@)

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  9. Show that sin 12^(@) sin 48^(@) sin 54^(@) = (1)/(8)

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  10. Show that cos (pi)/(15) cos""(2pi)/(15) cos"" (3pi)/(15) cos"" (4pi)/(...

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  11. Show that (sin 8x cos x - sin 6x cos 3x)/(cos 2x cos x - sin 3x sin 4x...

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  12. Show that ((cos theta - cos 3theta)(sin 8theta + sin 2 theta))/((sin 5...

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  13. Prove that sin x + sin 2x + sin 3x = sin 2x (1 + 2 cos x )

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  14. Prove that (sin 4x + sin 2x)/(cos 4x + cos 2x) = tan 3x.

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  15. Prove that 1 + cos 2x + cos 4x + cos 6x = 4 cos x cos 2x cos 3x

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  16. Prove that sin (theta)/(2) sin"" (7 theta)/(2) + sin ""(3theta)/(2) si...

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  17. Prove that cos(30^(@) -A ) cos (30^(@) + A ) + cos (45^(@) - A) cos (4...

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  18. Prove that (sin x + sin 3x + sin 5x + sin 7x)/(cos x + cos 3x + cos 5x...

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  19. Prove that (sin (4A - 2B) + sin (4B - 2A))/(cos (4A - 2B) + cos (4B - ...

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  20. Show that cot ( A + 15^(@)) - tan (A - 15^(@)) = (4 cos 2 A)/(1 + 2 si...

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