Question

Решите уравнения
cos2xcosx-sin2xsinx=√2/2
√x^2-П^2/16 * tg2x=0

Answer 1

1)cosacosb-sinasinb=cos(a+b)
cos3x=√2/2
3x=+-π/4+2πn
x=+-π/12+2πn/3)
2)ОДЗ x²-π²/16≥0
x²=π²/16⇒x=+-π/4
x≤-π/4 U x≥π/4
tg2x=0
2x=πn
x=πn/2 +ОДЗ⇒x=π+πn
Ответ x={-π/4;π/4;π+πn,n∈Z}