Question

Решите данное уравнение

Answer 1

$log_{16}(Sin^{2}x+3,5)=0,5\\\\Sin^{2}x+3,5=16^{0,5}\\\\Sin^{2}x+3,5=4\\\\Sin^{2}x=0,5\\\\Sin^{2}x=\frac{1}{2}\\\\Sinx=\pm\sqrt{\frac{1}{2}}=\pm\frac{\sqrt{2}}{2} \\\\1)Sinx=\frac{\sqrt{2}}{2}\\\\x=(-1)^{n}arcSin\frac{\sqrt{2}}{2}+\pi n,n\in Z\\\\x=(-1)^{n}\frac{\pi }{4}+\pi n,n\in Z$

$2)Sinx=-\frac{\sqrt{2}}{2}\\\\x=(-1)^{n}arcSin(-\frac{\sqrt{2}}{2})+\pi n,n\in Z\\\\x=(-1)^{n+1}\frac{\pi }{4}+\pi n,n\in Z$