\(\displaystyle{ \tg x + \ctg x = 3 \Longrightarrow \tg^{2} x + \ctg^{2} x =}\)
\(\displaystyle{ \tg x + \ctg x = 3 \iff \dfrac{\sin x}{\cos x} + \dfrac{\cos x}{\sin x} = 3 \iff \dfrac{\sin^{2} x + \cos^{2} x}{\sin x \cdot \cos x} = 3 \iff \dfrac{1}{\sin x \cdot \cos x} = 3 \iff \sin x \cdot \cos x = \frac{1}{3}}\)
\(\displaystyle{ \tg^{2} x + \ctg^{2} x = \dfrac{\sin^{2} x}{\cos^{2} x} + \dfrac{\cos^{2} x}{\sin^{2} x} = \dfrac{\sin^{4} x + \cos^{4} x}{\left( \sin x \cdot \cos x\right)^{2} } = \dfrac{\left( \sin^{2} x + \cos^{2} x\right)^{2} - 2\cdot \left( \sin x \cdot \cos x\right)^{2} }{\dfrac{1}{9}}}\)
moja odpowiedz to siedem
ona jest dobra?
