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Prove that (cos A - cos B) ^(2) + (sin A...

Prove that `(cos A - cos B) ^(2) + (sin A - sin B ) ^(2) = 4 sin ^(2) ((A -B)/( 2 )).`

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ICSE-COMPOUND AND MULTIPLE ANGLES -EXERCISE 5 (D)
  1. Prove that tan 2 A - sec A sin A = tan A sec 2 A.

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  2. Prove that (cos A + cos B ) ^(2) +(sin A + sin B) ^(2) = 4 cos ^(2) ((...

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  3. Prove that (cos A - cos B) ^(2) + (sin A - sin B ) ^(2) = 4 sin ^(2) (...

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  4. Prove that: cos ^(4) ""(pi)/(8) + cos ^(4) ""(3pi)/(8) + sin ^(4) "" (...

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  5. sin ^(4) "" (pi)/(8) + sin ^(4) "" (3pi)/(8) + sin ^(4) "" (5pi)/(8) +...

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  6. cos alpha cos(60^(@) - alpha ) cos (60^(@) + alpha ) = 1/4 cos 3 alpha...

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  7. (cos ^(3) alpha - cos 3 alpha )/( cos alpha ) + (sin ^(3)alpha + sin 3...

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  8. cos ^(2) 2 theta - sin ^(2) theta = cos theta . cos 3 theta.

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  9. 1 + (cos 2 theta + cos 6 theta)/(cos 4 theta) = (sin 3 theta)/(sin t...

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

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

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

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

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  14. 4 (cos ^(3) 20^(@) + cos ^(3) 40^(@)) = 3 ( cos 20 ^(@) + cos 40^(@))

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

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

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

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

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

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  20. 3 cos 72 ^(@) -4 sin ^(3) 18^(@) = cos 36 ^(@).

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