Rozwiąż równanie

[matshadow]

Rozwiąż równanie \(\displaystyle{ \tan^2\alpha_1+\tan^2\alpha_2+\cot^2\alpha_1+\cot^2\alpha_2=4}\)

[aga92]

Wskazówka:
\(\displaystyle{ \bigwedge\limits_{x\in R} tg^{2}x + ctg^{2} x qslant 2}\),

\(\displaystyle{ tg^{2} x + ctg^{2} x = 2 \iff tg^{2} x = ctg^{2} x}\)

[matshadow]

\(\displaystyle{ \frac{1}{\cot^2\alpha}=\cot^2\alpha}\)
\(\displaystyle{ \cot\alpha=-1\vee\cot\alpha=-1\Rightarrow\alpha=\frac-{\pi}{4}\vee\alpha=\frac{\pi}{4}}\)