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Prove that : tan^(-1)1+tan^(-1)2+tan^(-1...

Prove that : `tan^(-1)1+tan^(-1)2+tan^(-1)3=pi`

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`Tan^(−1)1+tan^ (−1) 2+tan^ (−1) 3`

`=tan^ (−1) 1+(tan^ (−1) 2+tan^ (−1) 3)`

`=tan^ (−1 )1+π+tan^ (−1)( (1−2×3)-:(2+3))`

`=tan^ (−1 )1+tan^ (−1 )−1+π`

`=(4-:π)+(4-:(−π))+π`

`=π`
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" (i) "tan^(-1)1+tan^(-1)2+tan^(-1)3=pi

Prove that : tan^(-1)1/5+tan^(-1)1/7+tan^(-1)1/3+tan^(-1)1/8=pi/4

Pove that i) tan^(-1)1/2+tan^(-1)2/11=tan^(-1)3/4 ii) tan^(-1)2/11+tan^(-1)7/24=tan^(-1)1/2 iii) tan^(-1)1+tan^(-1)1/2+tan^(-1)1/3=pi/2 iv) 2tan^(-1)1/3+tan^(-1)/17=pi/4 v) tan^(-1)2-tan^(-1)1=tan^(-1)1/3 vi) tan^(-1)+tan^(-1)2+tan^(-1)3=pi vii) tan^(-1)1/2+tan^(-1)1/5+tan^(-1)1/8=pi/4 viii) tan^(-1)1/4+tan^(-1)2/9=1/2tan^(-1)4/3

Prove that tan^(-1)1+tan^(-1)((1)/(2))+tan^(-1)((1)/(3))=(pi)/(2)

Prove that 2(tan^(-1)1/4+tan^(-1)2/9)=tan^(-1)4/3 .

Show that ( tan^(-1) 1 + tan^(-1) 2 + tan^(-1) 3) = pi

Prove that : tan^(-1)2+tan^(-1)3=(3pi)/4

Prove that : tan^(-1)2+tan^(-1)3=(3 pi)/(4)

Prove that : tan^(-1)(1/2) + tan^(-1)(1/3) = tan^(-1)(3/5) + tan^(-1)(1/4) = pi/4

Prove that tan^(-1)3/4+tan^(-1)3/5-tan^(-1)8/19=pi/4 .

RD SHARMA-INVERSE TRIGONOMETRIC FUNCTION-Solved Examples And Exercises
  1. Prove that: tan^(-1)(2/(11))+tan^(-1)(7/(24))=tan^(-1)(1/2)

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  2. Prove that : tan^(-1)2+tan^(-1)3=(3pi)/4

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  3. Prove that : tan^(-1)1+tan^(-1)2+tan^(-1)3=pi

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

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  5. If tan^(-1)2+tan^(-1)3+theta=pi find the value of thetadot

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

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  7. Prove that : tan^(-1)(1/2)+tan^(-1)(1/5)+tan^(-1)(1/8)=pi/4dot

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  8. tan^-1 (3/4) + tan^-1 (3/5) + tan^-1 (8/19)

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  9. Prove that : tan^(-1)(1/5)+tan^(-1)(1/7)+tan^(-1)(1/3)+tan^(-1)(1/8)=p...

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  10. Prove that : cot^(-1)7+cot^(-1)8+cot^(-1)18=cot^(-1)3

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

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

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

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

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

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

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

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

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

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

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