Question

If $\tan x=1\frac{1}{3}$, then the value of $4{\sin }^{2}x-3{\cos }^{2}x+2$ is $3\frac{12}{m}$, where the value of m is

Answer 1

$\tan x=\frac{4}{3}$
$\tan x=\frac{P}{B}=\frac{4}{3}$
Using Pythagoras Theorem,
$H^2=P^2+B^2$
$H^2=4^2+3^2$
$H=5$
Now, $4{\sin }^{2}x-3{\cos }^{2}x+2$
= $4(\frac{P}{H}{)}^2-3(\frac{B}{H}{)}^2+2$
= $4(\frac{4}{5}{)}^2-3(\frac{3}{5}{)}^2+2$
= $\frac{64}{25}-\frac{27}{25}+2$
= $\frac{64-27+50}{25}$
= $\frac{87}{25}$
= $3\frac{12}{25}$