I have to solve sec x = 4 − 2 tan^2 x, giving all solutions in the interval 0 ≤ x ≤ 180 , i have no idea where to start..... so far i changed the tan into sec^2-1, but i still cannot solve, i think they want me to use binomial expansion
I have to solve sec x = 4 − 2 tan^2 x, giving all solutions in the interval 0 ≤ x ≤ 180 , i have no idea where to start..... so far i changed the tan into sec^2-1, but i still cannot solve, i think they want me to use binomial expansion
$\displaystyle \frac{1}{\cos x}=4-2\cdot \frac{\sin^2 x}{\cos^2 x} \Rightarrow \frac{1}{\cos x}=4-2\cdot \frac{1- \cos^2 x}{\cos^2 x} \Rightarrow$
$\displaystyle \Rightarrow \cos x =4\cos^2 x-2+2\cos^2 x \Rightarrow 6\cos^2 x-\cos x-2=0$
Now substitute :
$\displaystyle \cos x=t$
and solve quadratic equation .
Oops! I did this and realized you already have the solution. At any rate here it is.