1)tg²(5x+π/3)=3
a)tg(5x+π/3)=√3⇒5x+π/3=π/3+πn⇒5x=-π/3+π/3+πn⇒5x=πn⇒x=πn/5
b)tg(5x+π/3)=-√3⇒5x+π/3=-π/3+πn⇒5x=-π/3-π/3+πn⇒5x=-2π/3+πn⇒
⇒x=-2π/15+πn/5
2)cos²(3x-π/6)=3/4
a)cos(3x-π/6)=√3/2
3x-π/6=π/6+2πn U 3x-π/6=-π/6+2πn
3x=π/6+π/6+2πn=π/3+2πn U 3x=π/6-π/6+2πn=2πn
x=π/9+2πn/3 U x=2πn/3
b)cos(3x-π/6)=-√3/2
3x-π/6=5π/6+2πn U 3x-π/6=-5π/6+2πn
3x=π/6+5π/6+2πn=π+2πn U 3x=π/6-5π/6+2πn=-2π/3+2πn
x=π/3+2πn/3 U x=-2π/9+2πn/9
3)sin²(3π/4-2x)=1
a)sin(3π/4-2x)=1⇒3π/4-2x=π/2+2πn⇒2x=3π/4-π/2+2πn⇒2x=π/4+2πn⇒x=π/8+πn
b)sin(3π/4-2x)=-1⇒3π/4-2x=-π/2+2πn⇒2x=3π/4+π/2+2πn⇒2x=5π/4+2πn⇒
⇒x=5π/8+πn
4)4cos²(5π/4-x)=1⇒cos²(5π/4-x)=1/4
a)cos(5π/4-x)=√2/2
5π/4-x=π/4+2πn U 5π/4-x=-π/4+2πn
x=5π/4-π/4+2πn U x=5π/4+π/4+2πn
x=π+2πn U x=3π/2+2πn