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

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

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To prove the identity \[ \frac{\sin x - \sin y}{\cos x + \cos y} = \tan\left(\frac{x - y}{2}\right), \] we will use the sum-to-product identities for sine and cosine. ...
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NCERT ENGLISH-TRIGONOMETRIC FUNCTIONS-All Questions
  1. Prove that:(cos9x-cos5x)/(sin17 x-sin3x)=-(sin2x)/(cos10 x)

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

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

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

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

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

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

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

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

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

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

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  12. Find the values of the trigonometric function sin 765^(@)

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  13. Find the values of the trigonometric function c o s e c(-1410^@).

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  14. cot^2pi/6+cose c(5pi)/6+3tan^2pi/6=6

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  15. 2sin^2(pi/6 )+c o s e c^2((7pi)/6)cos^2(pi/3)=3/2

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  16. sin^2pi/6+cos^2pi/3-tan^2pi/4=-1/2

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

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  18. Prove that:cos(pi/4-x)cos(pi/4-y)-sin(pi/4-x)sin(pi/4-y)=sin(x+y)

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  19. Find the value of : (i) sin75^o (ii) tan15^o

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  20. 2sin^2(3pi)/4+2cos^2pi/4+2sec^2pi/3=10

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