The number of real solutions of the equations tan -1-x2-3 x-2-cos -1-4 x-x2-3-

The correct option is C ZeroSince √(x^2 3x+2)≥ 0 ⇒ 0 ≤ tan^ 1 lt; √(x^2 3x+2) lt; π/2 Since √(4x x^2 3)≥ 0 ⇒ 0 ≤ cos^ 1√(4x x^2 3)≤π/2 ⇒ 0 lt; L.H.S ...

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Standard XII

Mathematics

Exponential Function (a^x)

The number of...

Question

The number of real solutions of the equations $t a n^{- 1} \sqrt{x^{2} - 3 x + 2} + c o s^{- 1} \sqrt{4 x - x^{2} - 3} = π$

One

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Two

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Zero

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Infinite

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Solution

The correct option is C Zero
Since $\sqrt{x^{2} - 3 x + 2} \geq 0 \Rightarrow 0 \leq t a n^{- 1} < \sqrt{x^{2} - 3 x + 2} < \frac{π}{2}$
Since $\sqrt{4 x - x^{2} - 3} \geq 0 \Rightarrow 0 \leq c o s^{- 1} \sqrt{4 x - x^{2} - 3} \leq \frac{π}{2}$
$\Rightarrow 0 < L . H . S < π \Rightarrow$ The given equation has no solution

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The number of real solutions of the equations tan−1√x2−3x+2+cos−1√4x−x2−3=π

The correct option is C ZeroSince √x2−3x+2≥0⇒0≤tan−1<√x2−3x+2<π2 Since √4x−x2−3≥0⇒0≤cos−1√4x−x2−3≤π2 ⇒0<L.H.S<π⇒ The given equation has no solution

The number of real solutions of the equations $t a n^{- 1} \sqrt{x^{2} - 3 x + 2} + c o s^{- 1} \sqrt{4 x - x^{2} - 3} = π$