Question

Solving Trig. Equations:

csc^2x-2cot^2x=0

Answer 1

`csc^2x-2cot^2x=0;\ D:x\\eq k\pi\ (k\in\mathbb{Z})\\\\(1)/(sin^2x)-2\cdot(cos^2x)/(sin^2x)=0\\\\(1-2cos^2x)/(sin^2x)=0\iff 1-2cos^2x=0\\\\-2cos^2x=-1\ \ \ /:(-2)\\\\cos^2x=(1)/(2)\\\\cosx=\sqrt(1)/(2)\ \vee\ cosx=-\sqrt(1)/(2)\\\\cosx=(\sqrt2)/(2)\ \vee\ cosx=-(\sqrt2)/(2)`



`x=(\pi)/(4)+2k\pi\ \vee\ x=-(\pi)/(4)+2k\pi\ \vee\ x=(3\pi)/(4)+2k\pi\ \vee\ x=-(3\pi)/(4)+2k\pi\\\\\\Answer:x=(\pi)/(4)+(k\pi)/(2)\ (k\in\mathbb{Z})`