Równania...

[zaba555]

1) \(\displaystyle{ ctg^{2}x - 3tg^{2}x = 2}\)

2) \(\displaystyle{ 2sin^{3}x - 3sinxcosx = 0}\)

3) \(\displaystyle{ 2sin^{5}x - 3sin^{3}x + sinx = 0}\)

4) \(\displaystyle{ cos^{2}x - 3sinxcosx + 1 = 0}\)

[setch]

1.
\(\displaystyle{ ctg^2x-\frac{3}{ctg^2x}-2=0\\
t=ctg^2x \quad t q 0\\
t+\frac{1}{t}-2=0}\)
3.
\(\displaystyle{ \sin x (5\sin ^4 x-3\sin^2 x+1)=0\\
\sin x =0 5\sin ^4 x-3\sin^2 x+1=0 \quad ft (t=\sin^2x t\in\right) \\
\sin x =0 5t^2-3t+1=0}\)

[zaba555]

Wszystko gicior tylko Ci sie troche cyferki i znaki pomylily gdzieniegdzie:

1.
powinno byc
\(\displaystyle{ t - \frac{3}{t} -2 = 0}\)

3.
i tutaj
\(\displaystyle{ sinx(2sin^{4}x - 3sin^{2}x + 1) = 0}\)

ale i tak wielkie propsy

a te 2 pozostale ukuje ktos?

[Lady Tilly]

2)
\(\displaystyle{ sinx(2sin^{2x}-3cosx)=0}\)
\(\displaystyle{ sinx[2(1-cos^{2}x)-3cosx]=0}\)
\(\displaystyle{ sinx=0 2(1-cos^{2}x)-3cosx=0}\)