Question

Solve for x: ${\sin }^{2}x+{\cos }^2{30}^0=\frac{5}{4},wherex{0}^0\le x\le {90}^0$

Answer 1

We have,

${\sin }^{2}x+{\cos }^2{30}^0=\frac{5}{4}$

${\sin }^{2}x+\frac{3}{4}=\frac{5}{4}$

${\sin }^{2}x=\frac{5-3}{4}$

${\sin }^{2}x=\frac{2}{4}$

${\sin }^{2}x=\frac{1}{2}$

$\sin x=\pm \frac{1}{\sqrt{2}}$

$x={45}^0,{135}^0$

Since, $where{0}^0\le x\le {90}^0$

So,

$x={45}^0$

Hence, this is the answer.