If ${\tan ^2}\,\,{\rm{\theta }} - \left( {1 + \sqrt 3 } \right)\tan \,\,{\rm{\theta }} + \sqrt 3 = 0$, then the general value of ${\rm{\theta }}$ is

JEE MATHEMATICS MCQ: TRIGONOMETRIC EQUATIONS

1 Easy

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Application +4 | -1

{\tan ^2}\,\,\mathrm{\theta } - \left( {1 + \sqrt 3 } \right)\tan \,\,\mathrm{\theta } + \sqrt 3 = 0

, then the general value of

\mathrm{\theta }

View answer and explanation

Correct option: A

n\pi \,\, + \,\,\frac{\pi }{4},\;\,n\pi \,\, + \,\,\frac{\pi }{3}

Option A (

n\pi \\; + \\; \frac{\pi }{{4}},\\;n\pi \\; + \\; \frac{\pi }{{3}}

) is correct because it represents the general solutions obtained by solving the quadratic equation in

\tan \theta

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

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

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

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

\mathrm{X}

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

\tan \frac{x}{2}

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0 < x < \pi

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

\tan x