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

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

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As we know
`tan^(-1)x+tan^(-1)y=tan^(-1)((x+y)/(1-xy))`
`=> tan^(-1)((2x+3x)/(1-2x*3x))=(pi)/4`
`(5x)/(1-6x^2)=tan ((pi)/4)`
`(5x)/(1-6x^2)=1`
`5x=1-6x^2`
`6x^2 +5x -1=0`
`6x^2 +6x-x-1`
...
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RD SHARMA-INVERSE TRIGONOMETRIC FUNCTION-Solved Examples And Exercises
  1. If a > b > c >0 , prove that cot^(-1)((a b+1)/(a-b))+cot^(-1)((b c+1)...

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

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

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

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

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  6. Solve the equation: tan^(-1)sqrt(x^2+x)+sin^(-1)sqrt(x^2+x+1)=pi/2

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

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

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

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

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

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  12. 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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  13. Simplify [(3sin2alpha)/(5+3cos2alpha)] +tan^(-1)[(tanalpha)/4] ,w h e ...

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  14. Prove that: tan^(-1)(1/2tan2A)+tan^(-1)(cota)+tan^(-1)(cot^3A)={0,ifpi...

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  15. Prove that tan^-1(1/7)+tan^-1(1/13)=tan^-1(2/9)

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

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  17. Prove: tan^(-1)(1/4)+tan^(-1)(2/9)=sin^(-1)(1/(sqrt(5)))

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

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

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  20. Solve for x: tan^-1(x+1)+tan^-1(x-1)=tan^-1(8/31)

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