Question

If tan x = $1\frac{1}{3},$ find the value of : $4si{n}^{2}x-3co{s}^{2}x+2$

Answer 1

$\tan x=1\frac{1}{3}$
$\tan x=\frac{4}{3}$
$\tan x=\frac{P}{B}=\frac{4}{3}$
Using Pythagoras Theorem,
$H^2=P^2+B^2$
$H^2=3^2+4^2$
$H=5$
Now, $4{\sin }^{2}x-3{\cos }^{2}x+2$
$=4{\left(\frac{P}{H}\right)}^2-3{\left(\frac{B}{H}\right)}^2+2$
$=4{\left(\frac{4}{5}\right)}^2-3{\left(\frac{3}{5}\right)}^2+2$
$=\frac{64}{25}-\frac{27}{25}+2$
$=\frac{87}{25}$
$=3\frac{12}{25}$