Question

Without using mathematical tables, find the value of x, if
$2\cos e{c}^2{30}^0+x{\sin }^2{60}^0-\frac{3}{4}{\tan }^2{30}^0=10$

Answer 1

We have,

$2\cos e{c}^2{30}^0+x{\sin }^2{60}^0-\frac{3}{4}{\tan }^2{30}^0=10$

$2(2{)}^2+x{\left(\frac{\sqrt{3}}{2}\right)}^2-\frac{3}{4}{\left(\frac{1}{\sqrt{3}}\right)}^2=10$

$8+x\left(\frac{3}{4}\right)-\frac{3}{4}\left(\frac{1}{3}\right)=10$

$x\left(\frac{3}{4}\right)-\frac{1}{4}=2$

$x\left(\frac{3}{4}\right)=\frac{9}{4}$

$3x=9$

$x=3$

Hence, this is the answer.