sprawdź tożsamość

[drasza]

a) \(\displaystyle{ sin ^{2}= \frac{1}{ctg ^{2}+1 }}\)


b) \(\displaystyle{ \frac{tg}{ \sqrt{1+ tg ^{2} }}=sin}\)

[bakos3321]

a)
\(\displaystyle{ P=\frac{1}{\frac{cos^{2}x+sin^{2}x}{sin^{2}x}}=\frac{sin^{2}x}{cos^{2}x+sin^{2}x}=sin^{2}x}\)

[magdabp]

\(\displaystyle{ \frac{tgx}{\sqrt{1+tg^2x}}=\frac{tgx}{\sqrt{1+\frac{sin^2x}{cos^2x}}}=\frac{tgx}{\sqrt{\frac{cos^2x+sin^2x}{cos^2x}}}=\frac{tgx}{\sqrt{\frac{1}{cos^2x}}}=\frac{\frac{sinx}{cosx}}{\frac{1}{cosx}}=\frac{sinx}{cosx} cosx=sinx}\)