Udowodnij tożsamości

[Marek01]

a)\(\displaystyle{ sin2x-tgx=cos2xtgx}\)

b)\(\displaystyle{ 4sin^{4}+sin^{2}2x=4sin^{2}x}\)

c)\(\displaystyle{ \frac{cosx+ctgx}{ctgx}=1+sinx}\)

d)\(\displaystyle{ 1-tg^{2}x=\frac{cos2x}{cos^{2}x}}\)

[Nakahed90]

\(\displaystyle{ L=1-tg^{2}x=1-\frac{sin^{2}x}{cos^{2}x}=\frac{cos^{2}x-sin^{2}x}{cos^{2}x}=\frac{cos2x}{cos^{2}x}}\)

[Nakahed90]

\(\displaystyle{ L=\frac{cosx+ctgx}{ctgx}=\frac{cosx}{\frac{cosx}{sinx}}+1=sinx+1=P}\)

[jakbuj]

a)
\(\displaystyle{ L=2\sin x\cosx-\frac{\sin x}{\cos x}=\frac{2\sin x\cos ^{2}x-\sin x}{\cos x}=\frac{\sin x(2\cos^{2} x - 1)}{\cos x}=\tan x \cos2 x=P}\)