Question

# Which of the following is the solution set of the equation $$\displaystyle 2 \cos^{-1} \left ( x \right ) = \cot^{-1} \left ( \frac{2x^{2} - 1}{2x\sqrt{1-x^{2}}} \right )$$?

A
(0,1)
B
(1,1){0}
C
(1,0)
D
[1,1]

Solution

## The correct option is A $$\displaystyle \left ( 0, \: 1 \right )$$$$2cos^{ -1 }\left( x \right) =cos^{ -1 }\left( 2x^{ 2 }-1 \right)$$ for $$x\epsilon \left[ 0,1 \right]$$$$\Rightarrow cos^{ -1 }\left( 2x^{ 2 }-1 \right) =cot^{ -1 }\left( \cfrac { 2x^{ 2 }-1 }{ 2x\sqrt { 1-x^{ 2 } } } \right)$$ for $$x\epsilon \left( 0,1 \right)$$Mathematics

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