Помогите 4sin x+5 cos x=x4

Question

Помогите

4sin x+5 cos x=x4

Answer 1

8sinx/2cosx/2+5cos²x/2-5sin²x/2-4sin²x/2-4cos²x/2=0
9sin²x/2-6sinx/2cosx/2-cos²x/2=0  /cos²x/2≠0
9tg²x/2-6tgx/2-1=0
tgx/2=a
9a²-6a-1=0
D=36+36=72    √D=6√2
a1=(6-6√2)/18=(1-√2)/3⇒tgx/2=arctg(1-√2)/3+πn⇒x=2arctg(1-√2)/3+2πn
a2=(6+6√2)/18=(1+√2)/3⇒tgx/2=arctg(1+√2)/3+πn⇒x=2arctg(1+√2)/3+2πn