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Prove that: ((sin7x+sin5x)+(sin9x+sin3x)...

Prove that: `((sin7x+sin5x)+(sin9x+sin3x))/((cos7x+cos5x)+(cos9x+cos3x))=tan6x`

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To prove the identity \[ \frac{(\sin 7x + \sin 5x) + (\sin 9x + \sin 3x)}{(\cos 7x + \cos 5x) + (\cos 9x + \cos 3x)} = \tan 6x, \] we will use the sum-to-product identities for sine and cosine. ...
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NCERT ENGLISH-TRIGONOMETRIC FUNCTIONS-All Questions
  1. Find the degree measures corresponding to the following radian measur...

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  2. Prove that: sin 3x + sin 2x - sin x = 4 sin x cosx/2cos(3x)/2

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  3. Prove that: ((sin7x+sin5x)+(sin9x+sin3x))/((cos7x+cos5x)+(cos9x+cos3x)...

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  4. Prove that sinx + sin3x + sin5x+ sin7x=4cosxcos2xsin4x

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  5. Prove that: (cosx-cosy)^2+(sinx-siny)^2=4sin^2(x-y)/2

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  6. Prove that: (cosx+cosy)^2+(sinx-siny)^2=4cos^2(x+y)/2

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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