Write the value of ^ -1 (1 2 )+2 ^ -1 (1 2 ). - Vidyadip

Question

Write the value of $\cos^{-1}\Big(\frac{1}{2}\Big)+2\sin^{-1}\Big(\frac{1}{2}\Big).$

✓

Answer

$\cos^{-1}\Big(\frac{1}{2}\Big)+2\sin^{-1}\Big(\frac{1}{2}\Big)$
$=\frac{\pi}{3}+2\times\frac{\pi}{6}$
$\begin{Bmatrix}\text{Since},\cos^{-1}\text{x}=\text{An angle in }[0,\pi]\text{ whose cosin is x}\\\sin^{-1}\text{x}=\text{An angle in }\Big[-\frac{\pi}{2},\frac{\pi}{2}\Big]\text{ whose sine is x}\end{Bmatrix}$
$=\frac{\pi}{3}+\frac{\pi}{3}$
$=\frac{2\pi}{3}$
So,
$\cos^{-1}\Big(\frac{1}{2}\Big)+2\sin^{-1}\Big(\frac{1}{2}\Big)=\frac{2\pi}{3}.$

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