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Find the value of "cot"(pi/2-2"cot"^(-1)...

Find the value of `"cot"(pi/2-2"cot"^(-1)sqrt(3))`.

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The correct Answer is:
`sqrt(3)`
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ARIHANT PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS -Part II (QUESTIONS FOR PRACTICE)
  1. Evaluate "cos"("cosec"^(-1)13/12).

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  2. Write the value of "tan"(2"tan"^(-1)1/3).

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  3. Find the value of "cot"(pi/2-2"cot"^(-1)sqrt(3)).

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  4. Write the value of "tan"^(-1)(a/b)-"tan"^(-1)((a-b)/(a+b)).

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  5. Simplify "tan"^(-1)[sqrt((1-"cos"x)/(1+"cos"x))],xltpi.

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  6. Write "tan"^(-1)(("cos"x-"sin"x)/("cos"x+"sin"x)),xltpi in the simples...

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  7. Write "cot"^(-1)(1/(sqrt(x^(2)-1))),|x|gt1 in simplest form.

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

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  9. Show that "sin"^(-1)(8/17)+"sin"^(-1)(3/5)="cos"^(-1)(36/85).

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

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  11. Prove that "tan"^(-1)1/(2)+"tan"^(-1)1/(5)+"tan"^(-1)1/8=pi/(4).

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  12. Show that tan((1)/(2)"sin"^(-1)(3)/(4))=(4-sqrt(7))/(3).

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  13. Solve for x, cos (2sin^(-1)x)=(1)/(9), x gt 0.

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  14. If "sin"^(-1)(1-x)(1)-2"sin"^(-1)x=pi/(2), then find the value of x.

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  15. If "tan"^(-1)((x-2)/(x-4))+"tan"^(-1)((x+2)/(x+4))=pi/(4), then find t...

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  16. Solve for x, "tan"^(-1)((2x)/(1-x^(2)))+""cot"^(-1)((1-x^(2))/(2x))=...

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  17. Find the value of expression "sin"(2"tan"^(-1)1/(3))+"cos"("tan"^(-1...

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  18. Solve for x, 2 tan ^(-1)(cos x) =tan^(-1) (2"cosec"x).

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  19. If "tan"^(-1)a+"tan"^(-1)b+"tan"^(-1)c=pi, then prove that a+b+c=abc.

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  20. Solve for x, "tan"^(-1)x+2"cot"^(-1)x=(2pi)/(6).

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