The value of ${\rm{cose}}{{\rm{c}}^2}\,\,\frac{\pi }{2} + {\rm{cose}}{{\rm{c}}^2}\,\,\frac{{2\pi }}{7}\,\, + \,\,{\rm{cose}}{{\rm{c}}^2}\,\,\frac{{3\pi }}{7}$ is

JEE MATHEMATICS MCQ: TRANSFORMATIONS

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The value of

\mathrm{cose}{\mathrm{c}^2}\,\,\frac{\pi }{2} + \mathrm{cose}{\mathrm{c}^2}\,\,\frac{{2\pi }}{7}\,\, + \,\,\mathrm{cose}{\mathrm{c}^2}\,\,\frac{{3\pi }}{7}

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Correct option: D

{2^3}

Option D (

{2^3}

) is correct because the sum of the squares of the cosecant terms simplifies to 8 using trigonometric identities and properties of roots of trigonometric equations.

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