Question

If $\cos \theta =\frac{1}{2}(a+\frac{1}{a})$, then prove that
$\cos 3\theta =\frac{1}{2}(a^3+\frac{1}{a^3})$

Answer 1

$\cos$ $3\theta$ = 4 $co{s}^3\theta$ - 3 $\cos$ $\theta$
= cos $\theta$[4 $co{s}^2\theta$ - 3]
$=\frac{1}{2}(a+\frac{1}{a})[4.\frac{1}{a}{(a+\frac{1}{a})}^2-3]$
$=\frac{1}{2}(a+\frac{1}{a})[a^2+\frac{1}{a^2}-3]=\frac{1}{2}[a^3+\frac{1}{a^3}]$