If 4sin–1 x + cos–1 x = π, then what is the value of x?

1.	If 4sin–1 x + cos–1 x = π, then what is the value of x?
Answer» Given 4 sin^-1 x + cos^-1 x = π We know that sin^-1 x + cos^-1 x = π/2 \(\Rightarrow 4sin^{-1}x+\frac{\pi}{2}-sin^{-1}x=\pi\) \(\Rightarrow 3sin^{-1}x=\pi-\frac{\pi}{2}\) \(\Rightarrow 3sin^{-1}x=\frac{\pi}{2}\) \(\Rightarrow sin^{-1}x=\frac{\pi}{6}\) \(\Rightarrow sin^{-1}x=sin^{-1}\frac{1}{2}\) ∴ x = 1/2

Answer»

Given 4 sin^-1 x + cos^-1 x = π

We know that sin^-1 x + cos^-1 x = π/2

\(\Rightarrow 4sin^{-1}x+\frac{\pi}{2}-sin^{-1}x=\pi\)

\(\Rightarrow 3sin^{-1}x=\pi-\frac{\pi}{2}\)

\(\Rightarrow 3sin^{-1}x=\frac{\pi}{2}\)

\(\Rightarrow sin^{-1}x=\frac{\pi}{6}\)

\(\Rightarrow sin^{-1}x=sin^{-1}\frac{1}{2}\)

∴ x = 1/2

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