If `(sin^(-1)x)^(2)+(cos^(-1)x)^(2)=(5pi^(2))/(8)` then x =

Options

A. `pm 1`
B. `pm 1/2`
C. `-(1)/sqrt(2)`
D. none of these

Explanation

To solve the equation \((\sin^{-1} x)^2 + (\cos^{-1} x)^2 = \frac{5\pi^2}{8}\), we can follow these steps:

### Step 1: Use the identity for \(\cos^{-1} x\)
We know that:
\[ \cos^{-1} x = \frac{\pi}{2} - \sin^{-1} x \]
Substituting this into the equation gives:
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