5) 2*a-1=a+1
2a-a=1+1
a=2∈R
6) Formule: (A+B)^2=A^2+2AB+B^2
(A-B)^2=A^2-2AB+B^2
(2 sin x+3 cos x)^2=4sin^2x+12sinxcosx+9cos^2x
(3sinx-2cosx)^2=9sin^2-12sinxcosx+4cos^2
4sin^2x+12sinxcosx+9cos^2x+9sin^2-12sinxcosx+4cos^2=13
4sin^2x+4cos^2=4(sin^2x+cos^2x)=4*1=4
9sin^2x+9cos^2x=9(sin^2x+cos^2x)=9*1=9
Formula fundamentală a trigonometriei: sin^2x+cos^2x=1
Revenind la exercițiu:
12sinxcosx s-a redus cu -12sinxcos
4+9=13
13=13 (adevărat)
q.e.d.
