Помогите решить 4sin^2x -5sinxcosx - 6cos^x=0

Question

Помогите решить

4sin^2x -5sinxcosx - 6cos^x=0

Comments

6cos^2x

Answer 1

4sin²x -5sinxcosx - 6cos²x=0|:cos²x≠0
4tg²x-5tgx-6=0 |t=tgx
4t²-5t-6=0
D=(-5)²-4*4*(-6)=25+96=121=11²
t1=(5+11)/8=2                      t2=(5-11)/8=-0,75
tgx=2                                     tgx=-0,75
x=arctg2+πn, n∈Z                x=-arctg0,75+πn, n∈Z