The number of solutions of equation Sin − 1 ( x 2 − 1 ) + Cos − 1 ( 2 x 2 − 5 ) = 2 π is ____

Question

The number of solutions of equation Sin − 1 ( ​ x 2 − 1 ​ ) + Cos − 1 ( ​ 2 x 2 − 5 ​ ) = 2 π ​ is ____

TestHub · Accepted Answer

For the given equation to hold, we must have $∣ x^{2} - 1∣ = ∣2 x^{2} - 5∣$ . Solving this gives $x = \pm 2$ and $x = \pm 2$ . However, $x = \pm 2$ are extraneous. Therefore, the number of solutions is 2.

Final Answer: The final answer is $2$

Mathematics - Inverse Trigonometric Function Question with Solution | TestHub

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