Równania trygonometryczne

[ptasiek123]

a)
\(\displaystyle{ \cos(x+ \frac{ \pi }{6})=\sin2x}\)
b)
\(\displaystyle{ \tg x=\tg \frac{1}{x}}\)
c)
\(\displaystyle{ \cos x+\sin x= \frac{\cos 2x}{1-\sin 2x}}\)

[Pancernik]

\(\displaystyle{ \cos\alpha = \sin\left( \frac{\pi}{2} -\alpha\right)}\)

[octahedron]

\(\displaystyle{ b)\\
\tg x=\tg \frac{1}{x}\\
x=\frac{1}{x}+k\pi,\ k\in Z\\
x^2-k\pi x-1=0\\
\Delta =k^2\pi^2+4>0\\
x=\frac{k\pi-\sqrt{k^2\pi^2+4}}{2}\ \vee\ x=\frac{k\pi+\sqrt{k^2\pi^2+4}}{2}\\}\)