Question

If $\cos \theta =\frac{x}{2}$ , then $2(1+\cos 8\theta )$

• A. $(x^4-4x^2+2)$
• B. $(x^4-4x^2-2{)}^2$
• C. $(x^4-4x^2+2{)}^2$
• D. $(x^4+4x^2+2{)}^2$

Answer 1

The correct option is C $(x^4-4x^2+2{)}^2$

$2(1+cos8\Theta )=4co{s}^{2}4\Theta =4(2co{s}^{2}2\Theta -1{)}^2$
$=4\left(2\right(2co{s}^2\Theta -1{)}^2-1{)}^2$
$=(x^4-4x^2+2{)}^2$