If $A + B + C = \pi $, then $\sin \,\,2A + \sin \,\,2B + \sin \,\,2C = $

$4\,\,\cos \,\,A\,\,\cos \,\,B\,\,\cos \,\,C$

$2\,\,\sin \,A\,\,\sin \,\,B\,\,\sin \,\,C$

JEE MATHEMATICS MCQ: TRANSFORMATIONS

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Application +4 | -1

A + B + C = \pi

, then

\sin \,\,2A + \sin \,\,2B + \sin \,\,2C =

View answer and explanation

Correct option: A

4\,\,\sin \,\,A\,\,\sin \,B\,\,\sin \,\,C

Option A (

4 \sin A \sin B \sin C

) is correct because by using the sum-to-product trigonometric identities and the fact that

A + B + C = \pi

, the expression

\sin 2A + \sin 2B + \sin 2C

simplifies to

4 \sin A \sin B \sin C

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 \;