The number of solutions of 5cos2 - -3 sin 2 - 6sin-cos-7 in the interval -0-2- is

The equation can be rewritten as 5 (1+cos 2θ/2) 3 (1 cos 2θ/2)+3 sin 2θ =7 ⇒ nbsp; 4 cos 2 θ + 3 sin 2 θ =6 But 4 cos 2 θ + 3 sin 2 θ≤ 5 nbsp; So, there is ...

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Standard XIII

Mathematics

Equations of the Form acosθ+bsinθ = c

The number of...

Question

The number of solutions of $5 {cos}^{2} θ - 3 {sin}^{2} θ + 6 sin θ cos θ = 7$ in the interval $[0, 2 π]$ is

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Solution

The correct option is C $0$
The equation can be rewritten as
$5 (\frac{1 + cos 2 θ}{2}) - 3 (\frac{1 - cos 2 θ}{2}) + 3 sin 2 θ = 7$
$\Rightarrow 4 cos 2 θ + 3 sin 2 θ = 6$
$But 4 cos 2 θ + 3 sin 2 θ \leq 5$
So, there is no solution for the given equation.

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Similar questions

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The number of solutions of 5cos2θ−3sin2θ+6sinθcosθ=7 in the interval [0,2π] is

The correct option is C 0The equation can be rewritten as 5(1+cos2θ2)−3(1−cos2θ2)+3sin2θ=7 ⇒4cos2θ+3sin2θ=6 But 4cos2θ+3sin2θ≤5 So, there is no solution for the given equation.

The number of solutions of $5 {cos}^{2} θ - 3 {sin}^{2} θ + 6 sin θ cos θ = 7$ in the interval $[0, 2 π]$ is

The correct option is C $0$
The equation can be rewritten as
$5 (\frac{1 + cos 2 θ}{2}) - 3 (\frac{1 - cos 2 θ}{2}) + 3 sin 2 θ = 7$
$\Rightarrow 4 cos 2 θ + 3 sin 2 θ = 6$
$But 4 cos 2 θ + 3 sin 2 θ \leq 5$
So, there is no solution for the given equation.