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Prove that: tan^(-1)((1-x)/(1+x))-tan^(-...

Prove that: `tan^(-1)((1-x)/(1+x))-tan^(-1)((1-y)/(1+y))=sin^(-1)((y-x)/(sqrt((1+x^2)(1+y^2))))`

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Prove that : tan^(-1)((x-y)/(1+xy)) + tan^(-1)((y-z)/(1+yz)) + tan^(-1)( (z-x)/(1+zx)) = tan^(-1)((x^2-y^2)/(1+x^2y^2))+tan^(-1)((y^2-z^2)/(1+y^2z^2))+tan^(-1)((z^2-x^2)/(1+z^2x^2))

Prove that : tan^(-1) x+cot^(-1) y = tan^(-1) ((xy+1)/(y-x))

tan^(- 1) (1/(x+y)) +tan^(- 1) (y/(x^2+x y+1)) =cot^(- 1)x

Find the value of tan^(-1)(x/y)-tan^(-1)((x-y)/(x+y))

Find the value of tan^(-1)(x/y)-tan^(-1)((x-y)/(x+y))

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RD SHARMA ENGLISH-INVERSE TRIGONOMETRIC FUNCTION-All Questions
  1. Prove that : cot^(-1)7+cot^(-1)8+cot^(-1)18=cot^(-1)3

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  2. Simplify each of the following: tan^(-1)((a+b x)/(b-a x))

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  3. Prove that: tan^(-1)((1-x)/(1+x))-tan^(-1)((1-y)/(1+y))=sin^(-1)((y-x)...

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  4. If a > b > c >0 , prove that cot^(-1)((a b+1)/(a-b))+cot^(-1)((b c+1)...

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  5. Solve : tan^(-1)((x-1)/(x-2))+tan^(-1)((x+1)/(x+2))=pi/4

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  6. Solve : tan^(-1)2x+tan^(-1)3x=pi/4

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  7. Solve: tan^(-1)((x-1)/(x+1))+tan^(-1)((2x-1)/(2x+1))=tan^(-1)((23)/(36...

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  8. If a ,\ b ,\ c >0 such that a+b+c=a b c , find the value of tan^(-1)a+...

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  9. Evaluateint(2-x)(5-x)\dx

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  10. If a1,\ a2,\ a3,\ ,\ an are in arithmetic progression with common ...

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  11. Prove that : sum(m=1)^n\ \ \ tan^(-1)((2m)/(m^4+m^2+2))=tan^(-1)((n^2+...

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  12. Sum the following series to infinity : tan^(-1)(1/(1+1+1^2))+tan^(-...

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  13. If ci >0 for i=1,\ 2,\ ,\ n , prove that tan^(-1)((c1x-y)/(c1y+x))+t...

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  14. If tan ^(-1 )""(yz )/( xr ) + tan ^(-1 )""(zx)/(yr) + tan ^(-1) "...

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  15. If a , b , c >0 and s=(a+b+c)/2,p rov et h a t tan^(-1)sqrt((2a s)/(b...

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  16. Simplify tan^-1[(3 sin 2alpha)/(5+3 cos2 alpha)]+tan^(-1)[(tan alpha)/...

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  17. Prove that: tan^(-1)(1/2tan2A)+tan^(-1)(cotA)+tan^(-1)(cot^3A)=0

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  18. Evaluateint5e^(7x)\dx

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  19. Prove that: sin^(-1) (12/13)+cos^(-1) (4/5)+tan^(-1) (63/16)=pi

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  20. Evaluateint\x^5(2-x)\dx

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