The general value of ${\rm{\theta }}$ satisfying ${\sin ^2}\,\,{\rm{\theta }} + \sin \,\,{\rm{\theta }} = 2$ is

$n\pi + {\left( { - 1} \right)^n}\,\,\frac{\pi }{6}$

$2n\pi \,\, + \,\,\frac{\pi }{4}$

$n\pi \,\, + \,\,{\left( { - 1} \right)^n}\,\,\frac{\pi }{3}$

JEE MATHEMATICS MCQ: TRIGONOMETRIC EQUATIONS

1 Easy

1 of 1

Application +4 | -1

The general value of

\mathrm{\theta }

satisfying

{\sin ^2}\,\,\mathrm{\theta } + \sin \,\,\mathrm{\theta } = 2

View answer and explanation

Correct option: C

n\pi \,\, + \,\,{\left( { - 1} \right)^n}\,\,\frac{\pi }{2}

Option C (

n\pi \\, + \\,{{\left( { - \\,1} \right)}^n}\frac{\pi }{2}

) is correct because it represents the general solution to the equation

\sin^2 \theta + \sin \theta = 2

Practice All Chapter MCQs →

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

\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}

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

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

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

\tan \frac{x}{2}

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

0 < x < \pi

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

\tan x