Simplify "tan"^(-1)[sqrt((1-"cos"x)/(1+"...

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

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The correct Answer is:

`x/(2)`

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ARIHANT PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS -Part II (QUESTIONS FOR PRACTICE)

Find the value of "cot"(pi/2-2"cot"^(-1)sqrt(3)).
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Write the value of "tan"^(-1)(a/b)-"tan"^(-1)((a-b)/(a+b)).
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Simplify "tan"^(-1)[sqrt((1-"cos"x)/(1+"cos"x))],xltpi.
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Write "tan"^(-1)(("cos"x-"sin"x)/("cos"x+"sin"x)),xltpi in the simples...
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Write "cot"^(-1)(1/(sqrt(x^(2)-1))),|x|gt1 in simplest form.
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Prove that "tan"^(-1)(1/4)+"tan"^(-1)(2/9)=1/2"tan"^(-1)(4/3).
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Show that "sin"^(-1)(8/17)+"sin"^(-1)(3/5)="cos"^(-1)(36/85).
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If "tan"^(-1)x+"tan"^(-1)y=pi/4,xylt1, then write the value of x+y+x...
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Prove that "tan"^(-1)1/(2)+"tan"^(-1)1/(5)+"tan"^(-1)1/8=pi/(4).
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Show that tan((1)/(2)"sin"^(-1)(3)/(4))=(4-sqrt(7))/(3).
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Solve for x, cos (2sin^(-1)x)=(1)/(9), x gt 0.
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If "sin"^(-1)(1-x)(1)-2"sin"^(-1)x=pi/(2), then find the value of x.
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If "tan"^(-1)((x-2)/(x-4))+"tan"^(-1)((x+2)/(x+4))=pi/(4), then find t...
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Solve for x, "tan"^(-1)((2x)/(1-x^(2)))+""cot"^(-1)((1-x^(2))/(2x))=...
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Find the value of expression "sin"(2"tan"^(-1)1/(3))+"cos"("tan"^(-1...
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Solve for x, 2 tan ^(-1)(cos x) =tan^(-1) (2"cosec"x).
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If "tan"^(-1)a+"tan"^(-1)b+"tan"^(-1)c=pi, then prove that a+b+c=abc.
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Solve for x, "tan"^(-1)x+2"cot"^(-1)x=(2pi)/(6).
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Prove that (9pi)/(8) -(9)/(4) sin^(-1)((1)/(3)) =(9)/(4) sin^(-1)((2sq...
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Prove that following cot^(-1)((xy+1)/(x-y)) +cot^(-1)((yz+1)/(y-z))+...
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