Question

If $11{\sin }^{2}x+7{\cos }^{2}x=8$ then $x=$______

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

Answer 1

Answer: (A)

$nx\pm \frac{\pi }{6},\forall n\in Z$

Given $11{\sin }^{2}x+7{\cos }^{2}x=8$

$⟹11{\sin }^{2}x+7-7{\sin }^{2}x=8$

$⟹4{\sin }^{2}x=1$

$⟹{\sin }^{2}x=\frac{1}{4}$

$⟹{\sin }^{2}x={\sin }^2\frac{\pi }{6}$

$⟹x=n\pi \pm \frac{\pi }{6},\forall Z$