Question

Solve the following equations
${\tan }^{2}33x=\cos 2x-1.$

Answer 1

${\tan }^{2}33x=\cos 2x-1$ [ Given ]

We know,

$\cos 2x=1-2{\sin }^{2}x$ by substituting in the equation we get

$\therefore$ ${\tan }^{2}33x=-2{\sin }^{2}x$

Both are squares of a trigonometric functions it means both are positive

$\therefore$ In order to satisfy the equation the only solution is

$\tan 33x=\sin x=0$

Implies, $x=n\pi$, where $n$ belongs to natural numbers