If $\;x\,\,\cos \,\,{\rm{\theta }} = y\,\,\cos \left( {{\rm{\theta }} + \frac{{2\pi }}{3}} \right) = {\rm{z}}\,\,\cos \left( {{\rm{\theta }} + \frac{{4\pi }}{3}} \right)\;$, then the value of $\frac{1}{x} + \frac{1}{y} + \frac{1}{{\rm{z}}}$ is equal to

JEE MATHEMATICS MCQ: MULTIPLE AND SUBMULTIPLE ANGLES

1 Easy

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Application +4 | -1

\;x\,\,\cos \,\,\mathrm{\theta } = y\,\,\cos \left( {\mathrm{\theta } + \frac{{2\pi }}{3}} \right) = \mathrm{z}\,\,\cos \left( {\mathrm{\theta } + \frac{{4\pi }}{3}} \right)\;

, then the value of

\frac{1}{x} + \frac{1}{y} + \frac{1}{\mathrm{z}}

is equal to

View answer and explanation

Correct option: C

Option C (0) is correct because the sum of the cosines with the given phase shifts equals zero, leading to the result 1/x + 1/y + 1/z = 0.