The value of - for which the area of the triangle formed by the line x sin-y cos-4 and the coordinate axis is minimum is

The correct option is A π4 Area of the OAB = 12×4sinθ×4cosθ nbsp;= 16sin 2θ Area of the triangle will be minimum when nbsp; sin 2θ nbsp; = 1 ⇒ 2θ nbsp ...

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Standard XII

Mathematics

Tangent To a Parabola

The value of ...

Question

The value of $θ$ for which the area of the triangle formed by the line $x sin θ + y cos θ = 4$ and the coordinate axis is minimum is

\frac{π}{2}

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\frac{π}{4}

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\frac{π}{3}

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\frac{π}{6}

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Solution

The correct option is B $\frac{π}{4}$

Area of the $△ O A B$
$= \frac{1}{2} \times \frac{4}{sin θ} \times \frac{4}{cos θ} = \frac{16}{sin 2 θ}$
Area of the triangle will be minimum when
$sin 2 θ = 1 \Rightarrow 2 θ = \frac{π}{2} \Rightarrow θ = \frac{π}{4}$

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The value of θ for which the area of the triangle formed by the line xsinθ+ycosθ=4 and the coordinate axis is minimum is

The correct option is B π4 Area of the △OAB =12×4sinθ×4cosθ=16sin2θ Area of the triangle will be minimum when sin2θ=1⇒2θ=π2⇒θ=π4

The value of $θ$ for which the area of the triangle formed by the line $x sin θ + y cos θ = 4$ and the coordinate axis is minimum is

The correct option is B $\frac{π}{4}$

Area of the $△ O A B$
$= \frac{1}{2} \times \frac{4}{sin θ} \times \frac{4}{cos θ} = \frac{16}{sin 2 θ}$
Area of the triangle will be minimum when
$sin 2 θ = 1 \Rightarrow 2 θ = \frac{π}{2} \Rightarrow θ = \frac{π}{4}$