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

If `a > b > c >0` , prove that `cot^(-1)((a b+1)/(a-b))+cot^(-1)((b c+1)/(b-c))+cot^(-1)((c a+1)/(c-a))=pi`

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RD SHARMA ENGLISH-INVERSE TRIGONOMETRIC FUNCTION-All Questions
  1. Simplify each of the following: tan^(-1)((a+b x)/(b-a x))

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  17. Evaluateint5e^(7x)\dx

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

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

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

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