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Prove that sin alpha + sin (120^(@) + ...

Prove that
`sin alpha + sin (120^(@) + alpha) + sin(240^(@)+ alpha)=0`

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If p sin alpha = q sin (120^(@) + alpha) = r sin (240^(@) + alpha),"prove that", pq + qr +rp = 0

Prove that cos alpha cos (120^(@) + alpha) cos (240^(@) + alpha) = 1/4 cos 3 alpha

Prove that, cos alpha + cos(120^(@) + alpha) + cos (120^(@) - alpha) = 0

Show that: sin^(3) alpha + sin^(3) (120^(@) + alpha) + sin^(3) (240^(@) + alpha)= - 3/4 sin 3 alpha

Prove that, sin^(2) alpha + sin^(2) (120^(@) - alpha) + sin^(2) (120^(@) + alpha) = 3/2

Prove that, cos^(3) alpha + cos^(3) (120^(@) + alpha) + cos^(3) (240^(@) + alpha) = 3/4 cos 3 alpha

Prove that, (1+ cos 2 alpha + sin 2 alpha)/(1-cos 2 alpha +sin 2 alpha)=cot alpha

Show that sin^3alpha+sin^3(120^@+alpha)+sin^3(240^@+alpha)=-3/4sin3alpha

If alpha=(pi)/(8 n) then prove that sin^(2) alpha+ sin^(2)3 alpha+ sin ^(2) 5 alpha+.. to 2n terms =n.

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CHHAYA PUBLICATION-TRANSFORMATIONS OF SUMS AND PRODUCTS-Short Answer Type Questions
  1. Prove that sin alpha + sin (120^(@) + alpha) + sin(240^(@)+ alpha)=0

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  2. Prove that sin 5 x cos 2x + cos 6 x sin 3 x = sin 8x cos x

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  3. Prove that sec(pi/4+theta)sec(pi/4-theta)=2 sec 2theta

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  4. Prove that cos (alpha+beta) +sin (alpha-beta)=2sin(pi/4+alpha)cos(pi...

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  5. Prove that 1 + (cos105^(@) + cos 165^(@))/(sin 105^(@) + sin 375^(@)...

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  6. Prove that sin 10^(@) + sin 50^(@)-sin70^(@)=0

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

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  8. Prove that cos(60^(@)+A) + cos(60^(@)-A)-cosA=0

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  9. Prove that "sin"((2pi)/3+theta)-"sin"((2pi)/3-theta) + sintheta=0

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  10. Prove that sin19^(@) + sin41^(@) + sin83^(@) = sin23^(@) + sin37^(@) ...

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  11. Prove that sin10^(@) + sin20^(@) + sin 40^(@) + sin 50^(@) = sin 70^(...

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  12. Prove that "cos" (3pi)/13 + "cos" (5pi)/13 - 2 "cos" (9pi)/13 "cos" (...

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  13. Prove that 4 sin 15^(@) sin 75^(@) = sqrt2 ( cos105^(@) + sin 75^(@)...

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  14. Prove that sin 80^(@) cos20^(@) + sin45^(@) cos145^(@)+sin 55^(@) co...

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  15. Prove that cos32^(@) sin20^(@) + cos144^(@) cos2^(@) + sin68^(@) cos...

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

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  17. Prove that cos 10^(@) cos20^(@) + sin 45^(@) cos145^(@) + sin 55^(@)...

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  18. Prove that cos24^(@) + cos 55^(@) + cos125^(@) +cos204^(@) + cos300^...

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

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  20. Prove that 8 sin20^(@) sin40^(@) sin80^(@) = sqrt3

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