The period of the function $f\left( x \right) = \frac{{\sin 8{\rm{x\;cosx}} - \sin 6{\rm{x\;cos}}3{\rm{x}}}}{{\cos 2{\rm{x}}\cos {\rm{x}} - \sin 3{\rm{x}}\sin 4{\rm{x}}}}$ is

JEE MATHEMATICS MCQ: TRANSFORMATIONS

1 Easy

1 of 1

Analyzing +4 | -1

The period of the function

f\left( x \right) = \frac{{\sin 8\mathrm{x\;cosx} - \sin 6\mathrm{x\;cos}3\mathrm{x}}}{{\cos 2\mathrm{x}\cos \mathrm{x} - \sin 3\mathrm{x}\sin 4\mathrm{x}}}

View answer and explanation

Correct option: C

\frac{\pi }{2}

Option C (

\frac{\pi}{{2}}

) is correct because the given function simplifies to

\tan 2x

, and the period of

\tan kx

\frac{\pi}{{|k|}}.

Practice All Chapter MCQs →

1 + \cos \,\,56^\circ + \cos \,\,58^\circ - \cos \,\,66^\circ = \lambda \cos \,\,28^\circ \,\,\cos \,\,29^\circ \,\,\sin \,\,33^\circ

\lambda =

\cos \,\,\frac{\pi }{{11}} + \cos \,\,\frac{{3\,\pi }}{{11}} + \cos \,\,\frac{{5\,\pi }}{{11}} + \cos \,\,\frac{{7\pi }}{{11}} + \cos \,\,\frac{{9\,\pi }}{{11}}

\;\cos \,\,x + \cos \,\,y + \cos \,\,\alpha = 0\;\,\mathrm{and}\,\sin x + \sin \,\,y + \sin \,\,\alpha = 0

\cot \left( {\frac{{x + y}}{2}} \right)\;

f\left( x \right) = \sin \left( {\frac{{2x + 3}}{{6\;\pi }}} \right),

0 < x,\mathrm{ }y < \pi

\cos x + \cos y - \cos (x + y) = \frac{3}{2}

\sin x + \cos y

\mathrm{\;sin}\,\,36^\circ \,\,\sin \,\,72^\circ \,\,\sin \,\,108^\circ \,\,\sin \,\,144^\circ \;