Question

Решить тригонометрические уравнения. 1. 2.

Answer 1

$1. cos^2(\frac{\pi}3-7x)=\frac12\\ a)cos(\frac{\pi}3-7x)=\frac1{\sqrt2}\\ \frac{\pi}3-7x=бarccos\frac1{\sqrt2}+2\pi n\\ \frac{\pi}3-7x=б\frac{\pi}4+2\pi n\\ -7x=б\frac{\pi}4-\frac{\pi}3+2\pi n \ |:(-7)\\ x_1=-\frac{\pi}{28}+\frac{\pi}{21}-\frac27\pi n \\ x_1=\frac{\pi}{21}-\frac{\pi}{28}-\frac27\pi n \\ x_1=\frac{\pi}{84}-\frac27\pi n \\ \\ x_2=\frac{\pi}{28}+\frac{\pi}{21}-\frac27\pi n \\ x_2=\frac{7\pi}{84}-\frac27\pi n \\ x_2=\frac{\pi}{12}-\frac27\pi n \\$

$b) cos(\frac{\pi}3-7x)=-\frac1{\sqrt2}\\ \frac{\pi}3-7x=бarccos(-\frac1{\sqrt2})+2\pi n\\ \frac{\pi}3-7x=б(\pi-\frac{\pi}4)+2\pi n\\ \frac{\pi}3-7x=б\frac{3\pi}4+2\pi n\\ -7x=б\frac{3\pi}4-\frac{\pi}3+2\pi n \ |:(-7)\\ x_3=-\frac{3\pi}{28}+\frac{\pi}{21}-\frac27\pi n \\ x_3=\frac{\pi}{21}-\frac{3\pi}{28}-\frac27\pi n \\ x_3=-\frac{5\pi}{84}-\frac27\pi n \\ \\ x_4=\frac{3\pi}{28}+\frac{\pi}{21}-\frac27\pi n \\ x_4=\frac{13\pi}{84}-\frac27\pi n \\$

$2. cos(sinx)=\frac12\\ sinx=б\frac{\pi}{3}+2\pi n\\ ??????((((($