Find the general solution for each of the following equation:
$cos 3 x + cos x - cos 2 x = 0$

x = (2 n + 1) \frac{π}{4}, n \in Z

No worries! We‘ve got your back. Try BYJU‘S free classes today!

x = 2 n π \pm \frac{π}{3}, n \in Z

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

x = - 2 n π \pm \frac{π}{3}, n \in Z

No worries! We‘ve got your back. Try BYJU‘S free classes today!

x = (2 n + 1) \frac{π}{3}, n \in Z

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $x = 2 n π \pm \frac{π}{3}, n \in Z$
The equation is
$c o s 3 x + c o s x - c o s 2 x = 0$

apply the formula $c o s A + c o s B = 2 c o s \frac{A + B}{2} \cdot c o s \frac{A - B}{2}$

$(c o s 3 x + c o s x) - c o s 2 x = 0$

$2 c o s \frac{3 x + x}{2} \cdot c o s \frac{3 x - x}{2} - c o s 2 x = 0$

$2 c o s 2 x \cdot c o s x - c o s 2 x = 0$

$c o s 2 x (2 c o s x - 1) = 0$

$c o s 2 x = 0$ or $c o s x = \frac{1}{2}$

For $c o s 2 x = 0$
$2 x = (2 n + 1) (\frac{π}{2})$
$x = (2 n + 1) (\frac{π}{4})$

For $c o s x = \frac{1}{2}$
$x = 2 n π \pm \frac{π}{3}$

where $n$ is any integer

Suggest Corrections