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Simplify 2"tan"^(-1)x+"sin"^(-1)((2x)/(1...

Simplify `2"tan"^(-1)x+"sin"^(-1)((2x)/(1+x^(2)))` in terms of `"tan"^(-1)x`.

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The correct Answer is:
`4"tan"^(-1)x`
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ARIHANT PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS -CHAPTER PRACTICE
  1. If "tan"^(-1)(sqrt(3))+"cot"^(-1)x=pi/(2), then find x.

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  2. If "tan"^(-1)x+"tan"^(-1)y=pi/4,xylt1, then write the value of x+y+x...

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  3. Simplify 2"tan"^(-1)x+"sin"^(-1)((2x)/(1+x^(2))) in terms of "tan"^(-1...

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  4. Find the value of "cos"^(-1)("cos"(5pi)/(3))+"sin"^(-1)("sin"(5pi)/(3)...

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  5. Find the value of 2"sec"^(-1)2+"sin"^(-1)(1/(2)).

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  6. Solve for x, "sin"^(-1)((2alpha)/(1+alpha^(2)))+"sin"^(-1)((2beta)/(...

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  7. Show that "sin"^(-1)(2xsqrt(1-x^(2)))=2"sin"^(-1)x.

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  8. Directions (Q. Nos. 16-25) Prove the following "cos"^(-1)x="tan"^(-1...

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  9. Directions (Q. Nos. 16-25) Prove the following 2"tan"^(1)1/(2)+"tan"...

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  10. Prove that tan^(-1)((1)/(5)) +tan^(-1)((1)/(7)) +tan^(-1)((1)/(3)) +...

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  11. Directions (Q. Nos. 16-25) Prove the following "sin"^(-1)(5/(13))+"c...

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  12. Directions (Q. Nos. 16-25) Prove the following "cos"["tan"^(-1){"sin...

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  13. Directions (Q. Nos. 16-25) Prove the following "cos"["sin"^(-1)(3/(5...

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  14. Directions Prove the following "tan"^(-1)1/(4)+"tan"^(-1)2/(9)=1/(2)...

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  15. Directions Prove the following "tan"^(-1)((sqrt(1+"cos"x)+sqrt(1-"c...

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  16. Prove the following "tan"^(-1)((1-x)/(1+x))-"tan"^(-1)((1-y)/(1+y))=...

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  17. Directions (Q. Nos. 16-25) Prove the following "cos"(2"tan"^(-1)1/(7...

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  18. Simplify the following: "tan"^(-1)[x/(sqrt(a^(2)-x^(2)))],|x|lta.

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  19. Solve the following equation: "cos"("tan"^(-1)x)="sin"("cot"^(-1)3/(...

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  20. Directions (Q. Nos. 27 and 28) Solve the following equations: "tan"...

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