The solution set of the equation \( (2 \cos x-1)(3+2 \cos x)=0 \) in \( 0 \leq x \leq 2 \pi \) is

\( \left\{\frac{\pi}{3}, \frac{\pi}{2}\right\} \)

\( \left\{\frac{\pi}{2}, \frac{3 \pi}{2}\right\} \)

\( \left\{\frac{\pi}{2}, \pi\right\} \)

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JEE MATHEMATICS MCQ: TRIGONOMETRIC EQUATIONS

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Application +4 | -1

The solution set of the equation

(2 \cos x-1)(3+2 \cos x)=0

0 \leq x \leq 2 \pi

View answer and explanation

Correct option: B

\left\{\frac{\pi}{3}, \frac{5 \pi}{3}\right\}

Option B ({π/3, 5π/3}) is correct because the equation (2cos(x)-1)(3+2cos(x))=0 implies cos(x) = 1/2 or cos(x) = -3/2. Since cos(x) cannot be -3/2, cos(x) = 1/2, which gives x = π/3 and x = 5π/3 in the given interval.

More Questions from TRIGONOMETRIC EQUATIONS

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The number of solutions of the equation

\sin \,\,x\,\,\;cos\,\,3x = \sin \,\,3x\,\,\cos \,\,5x

\left[ {0,\;\,\frac{\pi }{2}} \right]

is The number of ordered pairs

\left( {x,\,y} \right)

where

x,\,\,y \in \left[ {0,10} \right]

satisfying

\left( {\sqrt {{{\sin }^2} - \sin \,\,x + \frac{1}{2}} } \right){2^{{{\sec }^2}y}}\,\, \cdot \,\, \le 1

is Statement I: If slope of the tangent line is zero, then tangent line is perpendicular to the

\mathrm{X}

-axis.

Statement II: If

\theta \rightarrow \frac{\pi}{2}

, then tangent line is parallel to the Y-axis.
If

\sin x+\cos x=\frac{\sqrt{7}}{2}

, where

x \in\left[0, \frac{\pi}{4}\right]

, then

\tan \frac{x}{2}

is equal to The value of

\tan \frac{\pi}{5}+2 \tan \frac{2 \pi}{5}+4 \cot \frac{4 \pi}{5}

is If

0 < x < \pi

and

\cos x+\sin x=\frac{1}{2}

, then

\tan x

is equal to