System of equations : 2x, cos^2θ + y, sin2θ - 2sinθ = 0 x, sin2θ + 2y, sin^2θ = - 2, cosθ x, s

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3 and 4 .Determinants and Matrices

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The system of equations : $2x\, \cos^2\theta + y\, \sin2\theta - 2\sin\theta = 0$ $x\, \sin2\theta + 2y\, \sin^2\theta = - 2\, \cos\theta$ $x\, \sin\theta - y \cos\theta = 0$ , for all values of $\theta$ , can

A

have a unique non - trivial solution

B

not have a solution

C

have infinite solutions

D

have a trivial solution

Solution

slope of $(1)$ and $(2)$ is $\cot \theta$

$\Rightarrow$ $(1)$ and $(2)$ are parallel and slope of $(3)$ is $\tan\theta$ no solution.

Using $R_2 \rightarrow R_2 – (2 \cos\theta )$ $R_3$ and $R_1 \rightarrow R_1 + (2 \sin\theta )R_3$ , the value of determinat is $4$

Standard 12

Mathematics

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