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Solve the following.
If 4sin⁻¹x + cos⁻¹x = π, calculate the value of 'x'.
If $4\sin^{-1}x + \cos^{-1}x = \pi$, calculate the value of '$x$'.
Answer
Answer
Using $\cos^{-1}x=\frac\pi2-\sin^{-1}x$: $4\sin^{-1}x+\frac\pi2-\sin^{-1}x=\pi$
$3\sin^{-1}x=\frac\pi2$, so $\sin^{-1}x=\frac\pi6$
Hence $x=\sin\frac\pi6=\frac12$.
Final answer: $\frac{1}{2}$