If 0≤x≤1 and θ=Sin-1x+Cos-1x-Tan-1x then

x=0 ⇒θ=0+π2-0=π2 x=1 ⇒θ=π2+0-π4=π4 ⇒π4≤θ≤π2

If 0≤x≤1 and θ=Sin-1x+Cos-1x-Tan-1x then

x=0 ⇒θ=0+π2-0=π2 x=1 ⇒θ=π2+0-π4=π4 ⇒π4≤θ≤π2

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If $0 \leq x \leq 1$ and $θ = {Sin}^{- 1} x + {Cos}^{- 1} x - {Tan}^{- 1} x$ then

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$θ \leq π / 2$

$π / 4 \leq θ \leq π / 2$

$θ \geq π / 4$

$θ = π / 4$

answer is B.

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Detailed Solution

$x = 0 \Rightarrow θ = 0 + \frac{π}{2} - 0 = \frac{π}{2} x = 1 \Rightarrow θ = \frac{π}{2} + 0 - \frac{π}{4} = \frac{π}{4} \Rightarrow \frac{π}{4} \leq θ \leq \frac{π}{2}$

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