Hey, I'm stuck on these problems if anyone could help me it would be amazing!
tan^2x=3/2secx
sqrt3 sinx - cosx=sqrt3
#1 ...
$\displaystyle \tan^2{x} = \sec^2{x} - 1$ ... solve the resulting quadratic for $\displaystyle \sec{x}$
#2 ...
$\displaystyle \sqrt{3} \cdot \sin{x} = \cos{x} + \sqrt{3}$
square both sides ...
$\displaystyle 3\sin^2{x} = \cos^2{x} + 2\sqrt{3} \cdot \cos{x} + 3$
$\displaystyle 3(1 - \cos^2{x}) = \cos^2{x} + 2\sqrt{3} \cdot \cos{x} + 3$
solve the quadratic for $\displaystyle \cos{x}$