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Prove that: 2cospi/(13)cos(9pi)/(13)+cos...

Prove that: `2cos``pi/(13)``cos``(9pi)/(13)``+cos``(3pi)/(13)``+cos``(5pi)/(13)=0`

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To prove that \[ 2\cos\left(\frac{\pi}{13}\right)\cos\left(\frac{9\pi}{13}\right) + \cos\left(\frac{3\pi}{13}\right) + \cos\left(\frac{5\pi}{13}\right) = 0, \] we will use the cosine addition formula and properties of cosine. ...
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NCERT ENGLISH-TRIGONOMETRIC FUNCTIONS-All Questions
  1. Prove that: (cosx+cosy)^2+(sinx-siny)^2=4cos^2(x+y)/2

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  2. Prove that: (sin 3 x +sin x) sin x + (cos 3x - cos x) cos x = 0

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  3. Prove that: 2cospi/(13)cos(9pi)/(13)+cos(3pi)/(13)+cos(5pi)/(13)=0

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  4. Prove that:(cos4x+cos3x+cos2x)/(sin4x+sin3x+sin2x)=cot3x

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  5. Prove that:(sinx-sin3x)/(sin^2x-cos^2x)=2sinx

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  6. Prove that:tan4x=(4tanx(1-tan^2x))/(1-6tan^2x+tan^4x)

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  7. Prove that: cot x cot 2x - cot 2x cot 3x - cot 3x cot x = 1

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  8. Prove that:cos6x=32cos^6x-48cos^4x+18cos^2x-1

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  9. Prove that : cos 4x = 1 - 8 sin^2 x cos^2 x.

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  10. Find sinx/2,cosx/2 and tanx/2of the following : cotx=-1/3, x in quad...

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  11. Find sinx/2,cosx/2and tanx/2 of the following : tanx=-4/3, x in quadra...

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  12. Two trees, A and B are on the same side of a river. From a point C in ...

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  13. A tree stands vertically on a hill side which makes an angle of 15^0 w...

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  14. Two ships leave port at the same time. One goes 24 km per hour in the ...

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  15. For any triangle ABC, prove that(b^2 - c^2) cotA + (c^2 - a^2) cotB + ...

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  16. For any triangle ABC, prove that(b^2-c^2)/(a^2)sin2A+(c^2-a^2)/(b^2)si...

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  17. For any triangle ABC, prove that acosA+bcosB+c cosC=2asinBsinC

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  18. For any triangle ABC, prove that(cosA)/a+(cosB)/b+(cosC)/c=(a^2+b^2+c^...

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  19. In any triangle ABC, if a=18 , b=24 , c=30, findcosA, cosB, cosC

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  20. For any triangle ABC, prove that(a+b)/c=(cos((A-B)/2))/(sinC/2)

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