Question

8 cos 3 theta - 6 cos theta = 1 Prove theta = pie /9

Answer 1

Step-by-step explanation:

Question needs to be improved:

It should be written as:

$8cos^3\theta-6cos\theta=1$

If it is so, then let us prove it:

$8cos^3\theta-6cos\theta=1\\</p><p>\implies 2 (4cos^3\theta-3cos\theta)=1\\</p><p>\implies 2 (cos3\theta)=1</p><p>\implies cos3\theta= \frac{1}{2}\\</p><p>\implies cos3\theta= cos\frac{\pi}{3}\\</p><p>\implies 3\theta= \frac{\pi}{3}\\ </p><p>\implies \theta= \frac{\pi}{3\times 3}\\ </p><p>\implies \theta= \frac{\pi}{9}\\Thus \:proved.$

Formulae used:

$cos3\theta= 4cos^3\theta-3cos\theta\\</p><p>cos\frac{\pi}{3}=cos 60\degree =\frac{1}{2}$