If $\cos {\rm{\alpha }} + \cos {\rm{\beta }} + \cos {\rm{\gamma }} = \sin {\rm{\alpha }} + \sin {\rm{\beta }} + \sin {\rm{\gamma }} = 0,{\rm{\;then}}\cos 3{\rm{\alpha }} + \cos 3{\rm{\beta }} + \cos 3{\rm{\gamma \;}}$ equals

$3\cos \left( {{\rm{\alpha }} + {\rm{\beta }} + {\rm{\gamma }}} \right)$

$\cos \left( {{\rm{\alpha }} + {\rm{\beta }} + {\rm{\gamma }}} \right)$

$3\sin \left( {{\rm{\alpha }} + {\rm{\beta }} + {\rm{\gamma }}} \right)$

JEE MATHEMATICS MCQ: COMPLEX NUMBERS

1 Easy

1 of 1

Analyzing +4 | -1

\cos \mathrm{\alpha } + \cos \mathrm{\beta } + \cos \mathrm{\gamma } = \sin \mathrm{\alpha } + \sin \mathrm{\beta } + \sin \mathrm{\gamma } = 0,\mathrm{\;then}\cos 3\mathrm{\alpha } + \cos 3\mathrm{\beta } + \cos 3\mathrm{\gamma \;}

equals

View answer and explanation

Correct option: C

3\cos \left( {\mathrm{\alpha } + \mathrm{\beta } + \mathrm{\gamma }} \right)

Option C (

3\cos({\alpha} + {\beta} + {\gamma})

) is correct because using complex number representation and the condition

a+b+c=0

, we can derive the given trigonometric identity.