If $A + B + C\; = \frac{{3\,\pi }}{2}$, then $\cos \,\,2A + \cos \,\,2B + \cos \,\,2C$ is equal to

$1 - 4\;\cos A\,\,\cos B\,\,\cos C$

$1 + 2\cos A\,\,\cos B\,\,\cos C$

JEE MATHEMATICS MCQ: TRANSFORMATIONS

1 Medium

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Application +4 | -1

A + B + C\; = \frac{{3\,\pi }}{2}

, then

\cos \,\,2A + \cos \,\,2B + \cos \,\,2C

is equal to

View answer and explanation

Correct option: D

1 - 4\sin A\,\,\sin B\,\,\sin C

Option D (

1 - 4\sin A\sin B\sin C

) is correct because, with the given condition, the expression simplifies to this form using trigonometric identities.

Practice All Chapter MCQs →

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

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\sin x + \cos y

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