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Prove that cos ^(3) (x-(2pi)/(3)) + cos ...

Prove that `cos ^(3) (x-(2pi)/(3)) + cos ^(3) x + cos ^(3) (x + (2pi)/(3)) = (3)/(4) cos 3x. `

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ICSE-COMPOUND AND MULTIPLE ANGLES -EXERCISE 5 (D)
  1. cos ^(2) 2 theta - sin ^(2) theta = cos theta . cos 3 theta.

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  2. 1 + (cos 2 theta + cos 6 theta)/(cos 4 theta) = (sin 3 theta)/(sin t...

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  3. Prove that cos ^(3) (x-(2pi)/(3)) + cos ^(3) x + cos ^(3) (x + (2pi)/(...

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  4. (1)/(sin 10^(@)) - (sqrt3)/(cos 10 ^(@)) = 4.

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  5. tan 70^(@) -tan 20^(@) - 2 tan 40^(@) = 4 tan 10 ^(@).

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  6. tan theta + 2 tan 2 theta + 4 tan 4 theta + 8 cot 8 theta = cot theta.

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  7. 4 (cos ^(3) 20^(@) + cos ^(3) 40^(@)) = 3 ( cos 20 ^(@) + cos 40^(@))

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  8. Prove that 4(cos ^(3) 10^(@) + sin ^(3) 20^(@)) = 3 ( cos 10^(@) + sin...

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  9. Prove that cos ^(3) x sin ^(2) x = (1)/(16) (2cos x - cos 3x - cos 5x)...

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  10. cot A + cot (60^(@) + A) + cot (120^(@) +A) = 3 cot 3 A.

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  11. Prove that : cos 36 ^(@) - sin 18^(@) = (1)/(2).

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  12. cos ^(2) 36^(@) + sin ^(2) 18^(@) = (3)/(4).

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  13. 3 cos 72 ^(@) -4 sin ^(3) 18^(@) = cos 36 ^(@).

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  14. cos ^(2) 48^(@) - sin ^(2) 12 ^(@) = (sqrt5+1)/(8).

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  15. Prove that sin "" (1)/(10) pi cos ""(1)/(5) pi = (1)/(4).

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  16. sec 72 ^(@) - sec 36^(@) = 2.

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  17. sin ^(2) 24 ^(@) - sin ^(2) 6^(@) = (sqrt5 -1)/(8).

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  18. sin 12 ^(@) sin 48^(@) sin 54 ^(@) = (1)/(8).

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  19. Prove that 4 cos 6^(@) cos 42 ^(@) cos 66^(@) cos 78^(@) = (1)/(4).

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  20. sin "" (pi)/(5) sin "" (2pi)/(5) sin ""(4pi)/(5) sin""(3pi)/(5) = (5)/...

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