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Prove that 4 sin theta sin(pi/3 + thet...

Prove that
`4 sin theta sin(pi/3 + theta) sin (pi/3-theta) = sin 3 theta`

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CHHAYA PUBLICATION-TRANSFORMATIONS OF SUMS AND PRODUCTS-Short Answer Type Questions
  1. Prove that cos40^(@) cos80^(@) cos160^(@) = -1/8

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  2. Prove that cos thetacos(60^(@)- theta)cos(60^(@)+theta) = 1/4 cos 3 ...

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  3. Prove that 4 sin theta sin(pi/3 + theta) sin (pi/3-theta) = sin 3 th...

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  4. Prove that cos alpha cos (120^(@) + alpha) cos (240^(@) + alpha) = 1...

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  6. Find the value: sec20^(@) sec40^(@) sec80^(@)

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  7. Find the value: sqrt3 cot20^(@) cot40^(@)cot80^(@)

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  8. Find the value: 1/(2sin 10^(@))-2 sin 70^(@)

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  9. Prove the following identities : 4 sin 23^(@) sin37^(@) sin 83^(@) =...

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  10. Prove the following identities : cos2 A + cos 4A + cos 6A + cos8A =4...

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  11. Prove the following identities : (sin(A+B) - 2 sin A + sin (A-B))/(c...

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  12. Prove the following identities : (sin theta +sin 3 theta + sin 5 the...

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  13. If 13theta =pi " show that"cos 3 theta + cos 5 theta + 2 cos theta co...

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  14. If sin 2 alpha = 4 sin 2 beta, "show that", 5tan ( alpha -beta) = 3 ta...

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  15. If sin A = m sin B, "prove that" "tan" (A-B)/2 = (m-1)/(m+1) "tan" (A+...

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  17. If "cosec"A + secA = "cosec"B + sec B prove that "tan"(A+B)/2 = cot ...

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  18. If alpha,beta,gamma "are in A.P. show that" cot beta = (sin alpha - si...

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  19. If cot y =(sin(z+x))/(cos (z-x)-cos(z+x)),"show that" cot x , cot y "a...

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  20. If sinx + sin y = sqrt3 (cosy-cos x),"then show that" sin 3x+ sin 3y =...

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