Pokaż, że jeżeli...

[pool]

Pokaż, że jeżeli \(\displaystyle{ \cos\alpha=m}\)i \(\displaystyle{ m 0}\), to
a)\(\displaystyle{ (\sin\alpha * \cos\alpha)^2 = m^2 - m^4}\)
b)\(\displaystyle{ (\tan\alpha + \cot\alpha)^2 - \cot^2\alpha = \frac{m^2 +1}{m^2}}\)

[wb]

a)
\(\displaystyle{ (\sin\alpha * \cos\alpha)^2 = sin^2\alpha cos^2\alpha = (1-cos^2\alpha)cos^2\alpha=cos^2\alpha-cos^4\alpha =m^2 - m^4}\)

[ Dodano: 2 Grudnia 2007, 12:37 ]
b)
\(\displaystyle{ (\tan\alpha + \cot\alpha)^2 - \cot^2\alpha =tg^2\alpha+2tg\alpha ctg\alpha+ctg^2\alpha-ctg^2\alpha= \\ = \frac{sin^2\alpha}{cos^2\alpha}+2= \frac{1-cos^2\alpha+2cos^2\alpha}{cos^2\alpha}= \frac{1+cos^2\alpha}{cos^2\alpha}= \frac{m^2 +1}{m^2}}\)

[pool]

Zgadza się, dzięki WB