Question

The general solution of the equation $2\cos 2x=3.2{\cos }^{2}x−4$ is

• A. $x=2nÏ€,n∈I$
• B. $x=nÏ€,n∈I$
• C. $x=\frac{nÏ€}{4},n∈I$
• D. $x=\frac{nÏ€}{2},n∈I$

Answer 1

Answer: (B)

$2\cos 2x=6{\cos }^{2}x−4$
$⇒2\left(2{\cos }^{2}x−1\right)=6{\cos }^{2}x−4$
$⇒2{\cos }^{2}x=2⇒{\cos }^{2}x=1⇒x=nπ$