Sin^2x+3cosxsinx+1=0

Question

Sin^2x+3cosxsinx+1=0

Answer 1

Sin²x+3cosxsinx+1=0
2sin²x+3cosxsinx+cos²x=0  /cos²x≠0
2tg²x+3tgx+1=0
tgx=a
2a²+3a+1=0
D=9-8=1
a1=(-3-1)/4=-1⇒tgx=-1⇒x=-π/4+πn
a2=(-3+1)/4=-1/2⇒tgx=-1/2⇒x=-arctg0,5+πn