Number of values of θ in [0, 2π] satisfying equation 2{sin ^2}θ = 4 + 3 cos θ are

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Trigonometrical Equations

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The number of values of $\theta $ in $[0, 2\pi]$ satisfying the equation $2{\sin ^2}\theta = 4 + 3$$\cos \theta $ are

A

$0$

B

$1$

C

$2$

D

$3$

Solution

(a) $2 – 2{\cos ^2}\theta = 4 + 3\cos \theta $

$ \Rightarrow $ $2{\cos ^2}\theta + 3\cos \theta + 2 = 0$

$ \Rightarrow $ $\cos \theta = \frac{{ – 3 \pm \sqrt {9 – 16} }}{4}$,

which is imaginary, hence no solution.

Standard 11

Mathematics

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