Question

Реебят,, решить, надо) sin^2(3x-пи/8)=1/2

Answer 1

1)sin(3x-пи/8)=1/2                                           и              2)sin(3x-пи/8)= - 1/2

3х - pi/8 = (-1)^n (pi/6) +pin                                                3х - pi/8 = (-1)^(n+1) (pi/6) +pin  

3x = (-1)^n (pi/6) +pi/6+pin                                                  3x = (-1)^(n+1) (pi/6) +pi/6+pin   

x = (-1)^n (pi/18) +pi/18+pin /3                                             x = (-1)^(n+1) (pi/18) +pi/18+pin /3

Answer 2

$sin^2(3x-\frac{\pi}{8})=\frac{1}{2}\\ sin^2\alpha = \frac{1}{2}\\ \frac{1-cos2\alpha}{2}=\frac{1}{2}\\ 1-cos2\alpha=1\\ cos2\alpha=0\\ 2\alpha=\frac{\pi}{2}\\ \alpha = \frac{\pi}{4}\\ 3x-\frac{\pi}{8} = \frac{\pi}{4}\\ 3x = \frac{3\pi}{8}\\ x = \frac{\pi}{8}$