Question

The solutions of the equation $4{\cos }^{2}x+6{\sin }^{2}x=5$ are

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

Given, $4{\cos }^{2}x+6{\sin }^{2}x=5$
$\Rightarrow 4({\cos }^{2}x+{\sin }^{2}x)+2{\sin }^{2}x=5$
$\Rightarrow 2{\sin }^{2}x=5–4$
$\Rightarrow {\sin }^{2}x=\frac{1}{2}\Rightarrow {\sin }^{2}x={\sin }^2\frac{\pi }{4}$
$\Rightarrow x=n\pi \pm \frac{\pi }{4}$