Question

find the value of cos^-1(2x-1)

Answer 1

is this cos inverse (2x-1)
then the answer is , 2cos inverse √x.

Answer 2

The value of  $cos^{-1}(2x - 1) = 2cos^{-1}\sqrt{x}$

• We have,

         $cos^{-1}(2x - 1)$

        Let $x = cos^{2}\alpha$

        ∴ $\alpha$ = $cos^{-1}\sqrt{x}$     - (1)

• Now,

          $cos^{-1}(2x - 1) = cos^{-1}(2cos^{2}\alpha - 1)$

                                 $= cos^{-1}( cos2\alpha )$

                                $= 2\alpha$ ( As $cos^{-1}(cosA) = A$ )

• Now putting the value of $\alpha$ from (1) in the above equation, we get

          $cos^{-1}(2x - 1) = 2 cos^{-1}\sqrt{x}$

          ∴ the answer is $2cos^{-1}\sqrt{x}$