Q. $\cos{\alpha\sin{(\beta - \gamma)}} + \cos{\beta\sin{(\gamma - \alpha)}} + \cos{\gamma\sin{(\alpha - \beta)}}$ is equal to
A) 0
B) $\frac{1}{2}$
C) 1
D) $4\cos{\alpha\cos{\beta\cos\gamma}}$
Explanation
(a)
$\cos{\alpha\sin{(\beta - \gamma)}} + \cos{\beta\sin{(\gamma - \alpha)}} + \cos{\gamma\sin{(\alpha - \beta)}}$
=$\cos{\alpha{\lbrack sin}{\beta\cos{\gamma - \cos{\beta\sin{\gamma\rbrack}}}} + \cos{\beta\lbrack\sin{\gamma\cos{\alpha - \cos{\gamma\sin\alpha}}}\rbrack}} + \cos{\gamma\lbrack\sin{\alpha\cos{\beta - \cos{\alpha\sin\beta}}}\rbrack}$
$= 0$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.