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

Solve: `5tan^(-1)x+3cot^(-1)x=2pi`

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Given:
`5 tan ^{-1} x+3 cot ^{-1} x=2 pi`

We know that `tan ^{-1} x+cot ^{-1} x=frac{pi}{2} `

`implies cot ^{-1} x=frac{pi}{2}-tan ^{-1} x` ...
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RD SHARMA-INVERSE TRIGONOMETRIC FUNCTION-Solved Examples And Exercises
  1. Solve : 4sin^(-1)x=pi-cos^(-1)x

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

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

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  4. Prove that: tan^(-1)(2/(11))+tan^(-1)(7/(24))=tan^(-1)(1/2)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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