If $\;{\sin ^3}\,\,x\,\,\sin \,\,3x = \mathop \sum \limits_{m = 0}^n \,\,{c_m}\;\cos \,\,mx,\;\,{\rm{where}}\;\,{c_0},\,\,{c_{1\;}},\,\,{c_2}, \ldots ,\,{c_n}$ are constants and ${c_n} \ne 0$, then the value of $n$ is

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\;{\sin ^3}\,\,x\,\,\sin \,\,3x = \sum \limits_{m = 0}^n \,\,{c_m}\;\cos \,\,mx,\;\,\mathrm{where}\;\,{c_0},\,\,{c_{1\;}},\,\,{c_2}, \ldots ,\,{c_n}

are constants and

{c_n} \ne 0

, then the value of

n

View answer and explanation

Correct option: B

\mathrm{6}

Option B (6) is correct because expanding the expression

\sin^3 x \sin 3x

results in a cosine series with the highest multiple of x being 6.

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 \;