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Prove that (cos7x+cos5x)/(sin7x-sin5x)=c...

Prove that `(cos7x+cos5x)/(sin7x-sin5x)=cotx`.

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Here, we will use the following formulas:
`sin A - sin B = 2sin((A-B)/2)cos((A+B)/2)`
`cos A + cos B = 2cos((A-B)/2)cos((A+B)/2)`

`L.H.S. = (cos7x+cos5x)/(sin7x-sin5x)`
`=(2cos((7x+5x)/2)cos((7x-5x)/2))/(2cos((7x+5x)/2)sin((7x-5x)/2))`
`=cos(x)/sin(x)=cotx=R.H.S.`
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NCERT ENGLISH-TRIGONOMETRIC FUNCTIONS-All Questions
  1. Show that tan 3x tan 2x tan x = tan 3x - tan 2x - tan x.

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  2. Prove that (sin5x-2sin3x+sinx)/(cos5x-cosx)=tanx

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  3. Prove that (cos7x+cos5x)/(sin7x-sin5x)=cotx.

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  4. Prove that: sin (n + 1) x sin (n + 2)x + cos (n + 1) x cos (n + 2) x =...

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  5. Prove that: cos((3pi)/4+x)-cos((3pi)/4-x)=-sqrt(2)sinx

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  6. Prove that: sin^2 6x-sin^2 4x=sin2xsin10 x

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  7. Prove that:cos^2 2x-cos^2 6x=sin4xsin8x

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  8. Prove that:sin2x+2sin4x+sin6x=4cos^2xsin4

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  9. Prove that:cot 4x (sin 5x + sin 3x) = cot x (sin 5x - sin 3x)

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  10. Prove that:(cos9x-cos5x)/(sin17 x-sin3x)=-(sin2x)/(cos10 x)

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  11. Prove that:(sin5x+sin3x)/(cos5x+cos3x)=tan4x

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  12. Prove that:(sinx-siny)/(cosx+cosy)=tan(x-y)/2

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  13. Prove that:(sinx+sin3x)/(cosx+cos3x)=tan2x

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  14. Find the values of the trigonometric function tan (19pi)/3

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  15. Find the values of the trigonometric function sin (-(11pi)/3)

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  16. Find the value of other five trigonometric function cosx=-1/2, x lies...

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  17. Find the value of other five trigonometric function sinx=3/5, x lies ...

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  18. Find the value of other five trigonometric function cotx=3/4, x lies ...

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  19. Find the value of other five trigonometric function secx=(13)/5, x li...

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  20. Find the value of other five trigonometric function tanx=-5/(12), x l...

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