Question

If three angles A, B, C are such that cos A + cos B + cos C = 0 and if cos A cos B cos C $=\lambda (cos3A+cos3B+cos3C)$, then $\lambda$ is equal to

• A. $\frac{1}{12}$
• B. $\frac{1}{8}$
• C. $\frac{1}{4}$
• D. $\frac{1}{2}$

Answer 1

The correct option is A $\frac{1}{12}$

If $a+b+c=0\Rightarrow a^3+b^3+c^3=3abc$
So, $cosA.cosB.cosC=\lambda \left(4\right(co{s}^{3}A+co{s}^{3}B+co{s}^{3}C)-3(cosA+cosB+cosC\left)\right)$
$cosAcosBcosC=\lambda \left(4\right(3cosAcosBcosC\left)\right)$
$\lambda =\frac{1}{12}$