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Prove that cos40^(@) cos80^(@) cos160^...

Prove that
`cos40^(@) cos80^(@) cos160^(@) = -1/8`

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Prove that cos20^(@) cos40^(@) cos80^(@) = 1/8

Prove that cos 10^(@) + cos 110^(@) + cos 130^(@) = 0

Prove that cos306^(@) + cos234^(@) + cos162^(@) + cos18^(@) = 0

Prove that cos 80^(@) cos40^(@)+cos40^(@) cos200^(@) +cos200^(@) cos 80^(@) = -3/4

Prove that cos^(2)40^(@)cos^(2)80^(@)+cos^(2)80^(@)cos^(2)20^(@)+cos^(2)200^(@)cos^(2)40^(@)=(17)/(16)

Prove that cos24^(@) + cos 55^(@) + cos125^(@) +cos204^(@) + cos300^(@) = 1/2

Prove that, (cos30^(@) - sin 20^(@))/(cos 40^(@) + cos20^(@)) = 4/sqrt3 cos40^(@) cos 80^(@)

Prove that cos 10^(@) cos20^(@) + sin 45^(@) cos145^(@) + sin 55^(@) cos245^(@) = 0

Prove that, cos20^@cos40^@cos60^@cos80^@=1/16

Prove that cos 80^(@) - cos 40^(@) + sqrt3 cos 70^(@) = 0

CHHAYA PUBLICATION-TRANSFORMATIONS OF SUMS AND PRODUCTS-Short Answer Type Questions
  1. Prove that 8 sin20^(@) sin40^(@) sin80^(@) = sqrt3

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  2. Prove that tan20^(@) tan40^(@) tan80^(@) = sqrt3

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  3. Prove that cos40^(@) cos80^(@) cos160^(@) = -1/8

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

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

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

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  7. Find the value: sin 78^(@) - sin18^(@) + sin 30^(@) - sin42^(@)

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

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

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

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

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

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

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

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

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

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

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  18. If cos alpha = k cos beta , "show that", "tan" ( alpha+beta)/2 = ( 1-k...

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

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

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