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If cos A + cos B = (1)/(3) and sin A + s...

If `cos A + cos B = (1)/(3) and sin A + sin B = 1/4` prove that `tan "" (1)/(2) (A+B) = 3/4.`

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ICSE-COMPOUND AND MULTIPLE ANGLES -EXERCISE 5 (B)
  1. (sin 75^(@) - sin 15 ^(@))/( cos 75^(@) + cos 15 ^(@)) = (1)/(sqrt3)

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  2. (sin 7x + sin 3x )/(cos 7x + cos 3x ) = tan 5x.

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  3. (cos 2B - cos 2 A)/( sin 2 A + sin 2 B) = tan (A -B).

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  4. (sin (4A - 2B) + sin (4B - 2 A))/( cos (4 A - 2 B) + cos (4B - 2 A))= ...

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  5. (cos alpha + 2 cos 3 alpha + cos 5 alpha )/(cos 3 alpha + 2 cos 5 alph...

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  6. ( sin A + sin 3A + sin 5A + sin 7A)/(cos A + cos 3 A + cos 5 A + cos 7...

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  7. cos 20^(@) + cos 100^(@) + cos 140^(@) = 0

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  8. Prove that :sin 10^(@) + sin 20^(@) + sin 40^(@) + sin 50^(@) = sin 70...

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  9. Prove that cos 15 ^(@) - sin 15^(@) = (1)/(sqrt2)

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  10. Prove that sin 36 ^(@) + cos 36 ^(@) = sqrt2 cos 9^(@).

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  11. Prove that cos 20^(@) cos 40^(@) cos 80^(@) = (1)/(8).

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  12. sin 10 ^(@) sin 50^(@) sin 70^(@) = (1)/(8).

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  13. 4 cos 12 ^(@) cos 48^(@) cos 72^(@) = cos 36 ^(@)

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  14. tan 20^(@) tan 40^(@) tan 80^(@) = tan 60^(@)

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  15. 2 cos ""(pi)/(13) cos ""(9pi)/(13) + cos ""(3pi)/(13) + cos "" (5pi)/(...

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  16. tan (A + 30^(@)) + cot (A - 30^(@)) = (1)/( sin 2 A - sin 60^(@)).

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  17. cos A + cos (120 ^(@) - A ) + cos (120 ^(@) + A ) =0

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  18. cos (A +B) + sin (A -B) = 2 sin (45 ^(@) + A) cos ( 45 ^(@) + B).

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  19. If cos A + cos B = (1)/(3) and sin A + sin B = 1/4 prove that tan "" (...

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  20. What is the value of (cos 10 ^(@) + sin 20^(@))/( cos 20^(@) - sin 10 ...

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