Question

Решите уравнения: 1)sin²2x-sin4x=3cos²2x 2)3sin²3x+sin6x-cos²3x=0

Answer 1

1)sin²2x-sin4x=3cos²2x
sin²2x-2sin2xcos2x-3cos²2x=0|÷cos²2x≠0
tg²2x-2tg2x-3=0
tg2x=a
a²-2a-3=0
D=16
a=3; tg2x=3⇒2x=arctg3+πn; x=1/2*arctg3+πn/2
a=-1; tg2x=-1; 2x=-π/4+πk; x=-π/8+πk/2
2)3sin²3x+2sin3xcos3x-cos²3x=0|÷cos²3x≠0
3tg²3x+2tg3x-1=0
tg3x=a
3a²+2a-1=0
D=16
a=-1; tg3x=-1; 3x=-π/4+πn; x=-π/12+πn/3
a=2/3; 3x=arctg2/3+πk; x=1/3*arctg2/3+πk/3