Równania trygonometryczne w przedziałach

[xtrust]

\(\displaystyle{ (sinx-1)cosx=0}\)
\(\displaystyle{ ctg \frac{x}{2}-tg \frac{x}{2}=2tg \frac{x}{2}}\)
\(\displaystyle{ sinxsin3x= \frac{1}{2}}\)

[JHN]

\(\displaystyle{ (sinx-1)cosx=0}\)
\(\displaystyle{ sinx-1=0\ \ cosx=0}\)
\(\displaystyle{ sinx=1\ \ cosx=0}\)
\(\displaystyle{ (x={\pi\over 2}+k2\pi\ \ x={\pi\over 2}+k\pi\ )\ k\in C}\)
\(\displaystyle{ x={\pi\over 2}+k\pi\ \ k\in C}\)
Pozdrawiam

[xtrust]

dzieki , a pozostale ?:)

[Szemek]

\(\displaystyle{ ctg \frac{x}{2}-tg \frac{x}{2}=2tg \frac{x}{2}}\)
\(\displaystyle{ \frac{1+\cos x}{\sin x} - \frac{1-\cos x}{\sin x} = 2 \frac{1 -\cos x}{\sin x}}\)
\(\displaystyle{ \frac{2\cos x}{\sin x}=\frac{2-2\cos x}{\sin x}}\)
\(\displaystyle{ \frac{2\cos x - 2 + 2 \cos x}{\sin x}=0}\)
\(\displaystyle{ \frac{4\cos x-2}{\sin x}=0}\)
\(\displaystyle{ \cos x -\frac{1}{2} = 0 \sin x 0}\)
\(\displaystyle{ \cos x = \frac{1}{2} \sin x 0}\)
\(\displaystyle{ \left( x = \frac{\pi}{3} + 2k\pi x = -\frac{\pi}{3} + 2k\pi \right) k C}\)

[xtrust]

\(\displaystyle{ ctg \frac{x}{2} - tg \frac{x}{2}=2tgx \wedge x \in (-\pi;\pi>}\)
\(\displaystyle{ sinxsin3x= \frac{1}{2} \wedge x\in (-\pi; \frac{3}{2}\pi>}\)