Sprawdzenie tozsamosci

Bananowyraj · Post autor: **Bananowyraj** » 9 maja 2010, o 19:36

Bardzo prosze o pomoc I z gory dziekuje.

a) \(\displaystyle{ \tg\alpha + \ctg\alpha = \frac{1}{\sin\alpha\cos\alpha)}\)
b) \(\displaystyle{ (\tg\alpha – 1)(\ctg\alpha +1) = \tg\alpha – \ctg\alpha}\)

Lbubsazob · Post autor: **Lbubsazob** » 9 maja 2010, o 19:41

\(\displaystyle{ tg \alpha +ctg \alpha = \frac{sin \alpha }{cos \alpha }+ \frac{cos\alpha}{sin\alpha}= \frac{sin^2\alpha}{sin\alpha cos\alpha}+ \frac{cos^2\alpha}{sin\alpha cos\alpha}= \frac{1}{sin\alpha cos\alpha}}\)

agulka1987 · Post autor: **agulka1987** » 9 maja 2010, o 19:41

\(\displaystyle{ tg \alpha +ctg \alpha = \frac{sin \alpha }{cos \alpha } + \frac{cos \alpha }{sin \alpha } = \frac{sin^2 \alpha + cos^2 \alpha }{sin \alpha cos \alpha } = \frac{1}{sin \alpha cos \alpha }}\)

\(\displaystyle{ P=L}\)

\(\displaystyle{ (tg \alpha -1)(ctg \alpha +1) = 1 + tg \alpha -ctg \alpha -1 = tg \alpha -ctg \alpha}\)

\(\displaystyle{ P=L}\)