If the Quadratic equation 4sec2α.x2+2x+β2−β+12=0 has real roots, then the value ofcos2α+cos−1β is

Δ≥0⇒cos2α=1 &Δ≥0⇒cos2α=1

If the Quadratic equation 4sec2α.x2+2x+β2−β+12=0 has real roots, then the value ofcos2α+cos−1β is

Δ≥0⇒cos2α=1 &Δ≥0⇒cos2α=1

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If the Quadratic equation $4^{\sec^{2} α} . x^{2} + 2 x + (β^{2} - β + \frac{1}{2}) = 0$ has real roots, then the value of $\cos^{2} α + \cos^{- 1} β$ is

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$\frac{π}{2}$

$\frac{π}{2} - 1$

$\frac{π}{3}$

$\frac{π}{3} + 1$

answer is D.

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$Δ \geq 0 \Rightarrow \cos^{2} α = 1$ & $Δ \geq 0 \Rightarrow \cos^{2} α = 1$

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If the Quadratic equation 4sec2α.x2+2x+β2−β+12=0 has real roots, then the value ofcos2α+cos−1β is

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If the Quadratic equation $4^{\sec^{2} α} . x^{2} + 2 x + (β^{2} - β + \frac{1}{2}) = 0$ has real roots, then the value of $\cos^{2} α + \cos^{- 1} β$ is