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JEE Main202313 Apr 2023Evening ShiftMathematicsInverse Trigonometric FunctionsActual

For x ∈ ( - 1 , 1 ] , the number of solutions of the equation sin - 1 x = 2 tan - 1 x is equal to

Correct answer

0

Step-by-step solution

Given that sin - 1 x = 2 tan - 1 x ⇒ sin - 1 x = sin - 1 2 x 1 + x 2 ⇒ x = 2 x 1 + x 2 ⇒ x + x 3 = 2 x ⇒ x 3 - x = 0 ⇒ x ( x 2 - 1 ) = 0 ⇒ x = 0 , - 1 , 1 . But x ∈ ( - 1 , 1 ] , so the number of roots are 2 , x = 0   &   1

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