Question

The set of value(s) of $x$ for which $7{\cos }^{2}x+3{\sin }^{2}x=4$ is :

• A. $n\pi \pm \frac{\pi }{4},n\in Z$
• B. $n\pi \pm \frac{\pi }{6},n\in Z$
• C. $n\pi \pm \frac{\pi }{3},n\in Z$
• D. $2n\pi \pm \frac{\pi }{3},n\in Z$

Answer 1

The correct option is C $n\pi \pm \frac{\pi }{3},n\in Z$

$7{\cos }^{2}x+3{\sin }^{2}x=4\Rightarrow 7(1-{\sin }^{2}x)+3{\sin }^{2}x=4\Rightarrow 4{\sin }^{2}x=3\Rightarrow {\sin }^{2}x=\frac{3}{4}={\left(\frac{\sqrt{3}}{2}\right)}^2\Rightarrow {\sin }^{2}x={\sin }^2\frac{\pi }{3}\Rightarrow x=n\pi \pm \frac{\pi }{3},n\in Z$