The sum of all values of $x$ in $\left[ {0,\,\,2\pi } \right]$, for which $\sin x + \sin 2x + \sin 3x + \sin 4x = 0$, is equal to

JEE MATHEMATICS MCQ: TRIGONOMETRIC EQUATIONS

1 Easy

1 of 1

Analyzing +4 | -1

The sum of all values of

x

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

, for which

\sin x + \sin 2x + \sin 3x + \sin 4x = 0

, is equal to

View answer and explanation

Correct option: D

9\,\pi

Option D (

9\pi

) is correct because the sum of all solutions to the trigonometric equation within the given interval [0, 2

\pi

] is 9

\pi

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