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Range of $f(x) = \sin^{−1}x + \tan^{−1}x + \cos^{−1}x$ is |
$\left(0,\frac{3π}{2}\right)$ $\left(\frac{π}{2},\frac{3π}{2}\right)$ $\left(-\frac{π}{2},\frac{3π}{2}\right]$ $\left[\frac{π}{4},\frac{3π}{4}\right]$ |
$\left[\frac{π}{4},\frac{3π}{4}\right]$ |
$x ∈ [−1, 1]⇒\sin^{−1}x + \cos^{−1}x=\frac{π}{2}$ so $f(x)=\frac{π}{2}+\tan^{-1}x$ $\tan^{-1}x∈\left[-\frac{π}{4},\frac{π}{4}\right]$ $⇒\frac{π}{2}+\tan^{-1}x∈\left[\frac{π}{4},\frac{3π}{4}\right]$ |
