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Which of the following is the solution s...

Which of the following is the solution set of the equation `sin^-1 x = cos ^-1 x+ sin ^-1(3x-2)`

A

`[0,1/3]`

B

`[1/3,2/3]`

C

`[0,2/3]`

D

none of these

Text Solution

AI Generated Solution

To solve the equation \( \sin^{-1} x = \cos^{-1} x + \sin^{-1}(3x - 2) \), we will follow these steps: ### Step 1: Rewrite the Equation We start with the equation: \[ \sin^{-1} x = \cos^{-1} x + \sin^{-1}(3x - 2) \] Using the identity \( \cos^{-1} x = \frac{\pi}{2} - \sin^{-1} x \), we can rewrite the equation as: ...
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