Решите тригонометрические уравнения:1) cos 3x - √2/2 = 02) tg (x/2 + п/4) = -13) sin 2x + cos x = 04) cos 7x + cos x = 05) 2cos²x + 2sinx = 2,56) 1 + 2sin 2x + 2cos²x = 0

1) cos 3x - √2/2 = 0⇒cos3x=√2/2⇒3x=+-π/4+2πn⇒x=+-π/12+2πn/3 2) tg (x/2 + п/4) = -1⇒x/2+π/4=-π/4+πn⇒x/2=-π/2+πn⇒x=-π+2πn 3) sin 2x + cos x = 0⇒2sinxcosx+cosx=0⇒cosx(2sinx+1)=0 cosx=0⇒x=π/2+πn U sinx=-1/2⇒x=(-1)^n+1 *π/6+πn 4) cos 7x + cos x = 0⇒2cos4xcos3x=0 cos4x=0⇒4x=π/2+πn⇒x=π/8+πn/4 U cos3x=0⇒3x=π/2+πn⇒x=π/6+πn/3 5) 2cos²x + 2sinx = 2,5 2(1-sin²x)+ 2sinx = 2,5 2sin²x-2sinx+0,5=0 sinx=a 2a²-2a+0,5=0 4a²-4a+1=0 (2a-1)²=0 a=1/2⇒sinx=1/2⇒x=(-1)^n *π/6+πn 6) 1 + 2sin 2x + 2cos²x = 0 cos²x+sin²x+4sinxcosx+2cos²x=0 sin²x+4sinxcosx+3cos²x=0 /cos²x≠0 tg²x+4tgx+3=0 tgx=a a²+4a+3=0 a1+a2=-4 U a1*a2=3 a1=-3⇒tgx=-3⇒x=-arctg3+πn a2=-1⇒tgx=-1⇒x=-π/4+πn