If ${\rm{\;}}\cos \,\,\left( {{\rm{\theta }} - {\rm{\alpha }}} \right),\,\,\cos \,\,{\rm{\theta }}\,\,{\rm{and}}\,\,\cos \,\,\left( {{\rm{\theta }} + {\rm{\alpha }}} \right)$ are in HP, then $\cos \,\,{\rm{\theta }}\,\,\sec \,\,\frac{{\rm{\alpha }}}{2}$ is equal to

JEE MATHEMATICS MCQ: MULTIPLE AND SUBMULTIPLE ANGLES

1 Easy

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Application +4 | -1

\mathrm{\;}\cos \,\,\left( {\mathrm{\theta } - \mathrm{\alpha }} \right),\,\,\cos \,\,\mathrm{\theta }\,\,\mathrm{and}\,\,\cos \,\,\left( {\mathrm{\theta } + \mathrm{\alpha }} \right)

are in HP, then

\cos \,\,\mathrm{\theta }\,\,\sec \,\,\frac{\mathrm{\alpha }}{2}

is equal to

View answer and explanation

Correct option: A

\pm \,\sqrt 2

Option A (

\pm \\,\sqrt 2

) is correct because the expression simplifies to

\pm \\,\sqrt 2

when the given cosines are in Harmonic Progression.