Question

$4{\cos }^{2}x=3$ and $x$ is an acute angle, find the value of $m$ where ${\cos }^{2}x+{\cot }^{2}x$ =$3\frac{m}{4}$.

Answer 1

$4{\cos }^{2}x=3$

${\cos }^{2}x=\frac{3}{4}$

$\cos x=\frac{\sqrt{3}}{2}$

$\cos x=\cos 30$

$x={30}^{\circ }$

Thus, $\cot x=\cot 30=\sqrt{3}$

Now,

${\cos }^{2}x+co{t}^{2}x=\frac{3}{4}+3=\frac{3+12}{4}=\frac{15}{4}=3\frac{3}{4}$