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Prove that: sin(x+y)/sin(x-y)=(tanx+tany...

Prove that: `sin(x+y)/sin(x-y)=(tanx+tany)/(tanx-tany)`

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To prove that \[ \frac{\sin(x+y)}{\sin(x-y)} = \frac{\tan x + \tan y}{\tan x - \tan y} \] we will use the sine addition and subtraction formulas as well as the definition of tangent. ...
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RD SHARMA-TRIGONOMETRIC RATIOS OF COMPOUND ANGLES-Solved Examples And Exercises
  1. Prove that: cos(pi/4+x)+cos(pi/4-x\ )=sqrt(2)cosx

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

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  3. Prove that: sin(x+y)/sin(x-y)=(tanx+tany)/(tanx-tany)

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  4. Prove that (tan(pi/4+x))/(tan(pi/4-x))=((1+t a n x)/(1-t a n x))^2

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  5. if tanalpha=1/(sqrt(x(x^2+x+1))), tanbeta=(sqrtx)/(sqrt(x^2+x+1) and ...

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  6. Prove that :(tan(A+B))/("cot"(A-B))=(sin^2A-sin^2B)/(cos^2A-sin^2B)

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  7. Prove that : sin^2 6x-sin^2 4x=s in2x\ s in\ 10 x

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  8. Prove that: cos^2 2x-cos^2 6x=s in4x s in8x

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  9. Prove that: (cos^2 33^@-cos^2 57^)/(sin(21)^@-cos(21))=-1/sqrt(2)

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  10. Prove that: cos2alpha\ cos2beta+sin^2(alpha-beta)-sin^2(alpha+beta)=co...

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  11. Prove that: t a n 70^0=t a n 20^0+2t a n 50^0dot

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  12. If s inalpha+s inbeta=a\ a n d\ cosalpha+cosbeta=b , show that : cos(a...

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  13. If s inalpha+s inbeta=a\ a n d\ cosalpha+cosbeta=b , show that : cos(a...

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  14. If sinA=4/5a n dcosB=5/(13),\ w h e r e\ 0<A ,\ B<pi/2 , find the valu...

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  15. If sinA=4/5a n dcosB=5/(13),\ w h e r e\ 0<A ,\ B<pi/2 , find the valu...

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  16. If sinA=4/5a n dcosB=5/(13),\ w h e r e\ 0<A ,\ B<pi/2 , find the valu...

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  17. If sinA=4/5a n dcosB=5/(13),\ w h e r e\ 0<A ,\ B<pi/2 , find the valu...

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  18. If sinA=12/13 and sinB=4/5 where pi/2 < A < pi and 0 < B < pi/2 then f...

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  19. Prove that sinx/cos(3x)+sin(3x)/cos(9x)+sin(9x)/cos(27x)=1/2 (tan27x-t...

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  20. If s in A=3/5, cos B=-(12)/(13),\ w h e r e A and B both lie in second...

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