[tex]sin^{2}x + cos^{2}x = 1 \ \ \rightarrow \ \ sin^{2}x = 1 - cos^{2}x[/tex]
a)
[tex]L = (sinx + cosx)^{2}+(sinx-cosx)^{2}=\\\\=sin^{2}x + 2sinxcosx+cos^{2}x + sin^{2}x -2sinxcosx+cos^{2}x=\\\\=2(sin^{2}x + cos^{2}x) = 2\cdot1 = 2 = P[/tex]
b)
[tex]L = sin^{4}x - cos^{4}x = (sin^{2}x +cos^{2}x)(sin^{2}x - cos^{2}x) = 1\cdot(sin^{2}x - cos^{2}x)=\\\\=sin^{2}x - cos^{2}x = P[/tex]
c)
[tex]L = (tg^{2}x -sin^{2}x)\cdot ctg^{2}x=(\frac{sin^{2}x}{cos^{2}x}-sin^{2}x)\cdot\frac{cos^{2}x}{sin^{2}x} =\\\\=\frac{sin^{2}x cos^{2}x}{sin^{2}x cos^{2}x} -\frac{sin^{2}x cos^{2}x}{sin^{2}x} = 1 - cos^{2}x = sin^{2}x = P[/tex]
d)
[tex]L =\frac{1-cos^{2}x}{sinx cos x}=\frac{sin^{2}x}{sinx cos x} = \frac{sinx}{cosx} = tg x = P[/tex]
