Problem

Problem

If θ=sin⁡−1x+cos⁡−1x−tan⁡−1x,x≥0\theta = \sin^{-1} x + \cos^{-1} x - \tan^{-1} x, x \geq 0 then the smallest interval in which θ\theta lies is (a) π4≤θ≤3π4\frac{\pi}{4} \leq \theta \leq \frac{3\pi}{4} (b) 0≤θ≤π0 \leq \theta \leq \pi (c) −π4≤θ≤0-\frac{\pi}{4} \leq \theta \leq 0 (d) π4≤θ≤π2\frac{\pi}{4} \leq \theta \leq \frac{\pi}{2}

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