Równania trygonometryczne

[gabor94]

1.
\(\displaystyle{ \sin ^ 4 x+ \cos^4 x=\frac{5}{8}}\)
2.
\(\displaystyle{ \sin^3 x + \cos^3 x=1}\)
3.
\(\displaystyle{ \sin^2 x+\sin^2 2x=\sin^2 3x}\)
4.
\(\displaystyle{ \tg\left(\frac{3}{\pi}-x\right)-\tg x}\)
5.
\(\displaystyle{ \tg x+\tg 2x=\tg 3x}\)

[lorakesz]

1.
\(\displaystyle{ \sin ^ 4 x+ \cos^4 x=\frac{5}{8}\\
(\sin^2x+\cos^2x)^2-2\sin^2x\cos^2x=\frac{5}{8}\\
1-2\sin^2x\cos^2x=\frac{5}{8}\\
2\sin^2x\cos^2x=\frac{3}{8}\\
4\sin^2x\cos^2x=\frac{3}{4}\\
\sin^22x=\frac{3}{4}\\
\sin 2x=\frac{\sqrt{3}}{2}\quad \vee \quad \sin 2x=-\frac{\sqrt{3}}{2}\\}\)