3sin^2 x-4sinx * cos*x+5cos^2 x=2 Помогите

Question

3sin^2 x-4sinx * cos*x+5cos^2 x=2 Помогите

Answer 1

3sin²x-4sinxcosx+5cos²x-2sin²x-2cos²x=0
sin²x-4sinxcosx+3cos²x=0 /cos²x≠0
tg²x-4tgx+3=0
tgx=a
a²-4a+3=0⇒a1+a2=4 U a1*a2=3
a1=1⇒tgx=1⇒x=π/4+πn
a2=3⇒tgx=3⇒x=arctg3+πn

Comments

3sin²x-4sinxcosx+5cos²x-2sin²x-2cos²x=0 откуда -2sin²x-2cos²x?