Question

решить простейшие тригонометрические уравнения
1) cos 8x = 1
2) 2sin 6x = -√2
3) sin (3x+ π/10)=√3/2
4) tg4x = 1/√3
5) cos (2x + π/8)=0
6)tg(9x - π/12) =-1
7) cos7x * cos4x - sin7x * sin4x=1

Answer 1

$1);cos8x = 1\8x=2pi n,;;x=fracpi4n,;ninmathbb{Z}\ 2);2sin 6x = -sqrt2\sin6x=-frac{sqrt2}2\6x=frac{5pi}4+2pi n,;;x=frac{5pi}{24}+fracpi3n,;ninmathbb{Z}\ 3);sinleft(3x+fracpi{10}right)=frac{sqrt3}2\3x+fracpi{10}=fracpi3+2pi n\3x=frac{7pi}{30}+2pi n\x=frac{7pi}{90}+frac{2pi}3n,;;ninmathbb{Z}\ 4);tg4x = frac1{sqrt3}\4x=fracpi6+pi n\x=fracpi{24}+fracpi4n,;;ninmathbb{Z}$
$5);cos (2x + fracpi8)=0\2x+fracpi8=fracpi2+pi n\2x=frac{3pi}8+pi n\x=frac{3pi}{16}+fracpi2n,;;ninmathbb{Z}\ 6);tg(9x - fracpi{12}) =-1\9x-fracpi{12}=frac{3pi}4+pi n\9x=frac{10pi}{12}+pi n\x=frac{5pi}{54}+fracpi9n,;;ninmathbb{Z}\ 7);cos7xcdotcos4x - sin7xcdotsin4x=1\cos(7x+4x)=1\cos11x=1\11x=2pi n\x=frac{2pi}{11}n,;;ninmathbb{Z}$