An inequality with trigonometric functions
Task number: 2765
Solve \(\sin^2 x< \cos^2 x\) over the real domain.
Resolution
\(\sin^2 x < 1-\sin^2 x \longrightarrow \sin^2 x < \frac12 \longrightarrow |\sin x|< \frac{\sqrt2}{2}\).
Result
The solution is \(x\in \bigcup_{k\in \mathbb Z} (k\pi-\frac{\pi}4,k\pi+\frac{\pi}4)\).
