Rozwiązać równania.

[kaajteek]

a)\(\displaystyle{ cos(x- \frac{\pi}{6}) = sin2x}\)
b) \(\displaystyle{ 2sinx = 3ctgx}\)
c) \(\displaystyle{ tgx = sinx}\)
d) \(\displaystyle{ tgx = tg\frac{1}{x}}\)
e) \(\displaystyle{ cosx + sinx = \frac{cos2x}{1-sin2x}}\)
f) \(\displaystyle{ \frac{cosx}{1-sinx}= 1 + sinx}\)
g) \(\displaystyle{ 4sin^{4}x + sin^{2}2x = 2}\)
h) \(\displaystyle{ sin^{4}x + cos^{4}x = \frac{5}{8}}\)
i) \(\displaystyle{ sin(\frac{ \pi}{2} - x ) = cos({\pi} - x )}\)
j) \(\displaystyle{ 4sin^{2}x - sinxcosx + 3cos^{2}x = 3}\)
k) \(\displaystyle{ sinx*sin2x*sin3x = \frac{1}{4} * sin4x}\)

[Hondo]

c)
\(\displaystyle{ tgx = sinx}\)

\(\displaystyle{ \frac{sinx}{cosx}=sinx}\)

\(\displaystyle{ \frac{1}{cosx}=1}\)

\(\displaystyle{ cosx=1}\)

\(\displaystyle{ x=2 \pi n}\)