Question

Help me pleaseee!!!
4sin*x +sin2x=3
*-înseamnă la puterea a doua

Answer 1

4sin²x-3+2sinxcox=0
4sin²x-3sin²x-3cos²x+2sinxcosx=0
sin²x-3cos²x+2sinxcosx=0
impartim cu cos²x≠0 (pt cosx=0, avem x=(2k+1)π/2, ecuatia devine 4-3 +0=0⇒ 1=0 si nu are sens)

tg²x-3+2tgx=0
fie tgx=t
t²+2t-3=0
t1=-3...x =kπ+arctg(-3)
t2=1...x=kπ+arctg1=kπ+π/4

x∈kπ+π/4∪kπ+arctg(-3), k∈Z