1)
4x=±π/6+πn, n∈Z.
Ответ: x=±π/24+πn/4, n∈Z.
2)
x/5=±π/6+πn, n∈Z.
Ответ: x=±5π/6+5πn, n∈Z.
3)
Ответ: x=±arcsin(√15/6)+πn, n∈Z.
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1)![\sin^2{4x}=\frac{1}{4};|\sin{4x}|=\frac{1}{2}\\\sin{4x}=б\frac{1}{2} \sin^2{4x}=\frac{1}{4};|\sin{4x}|=\frac{1}{2}\\\sin{4x}=б\frac{1}{2}](https://tex.z-dn.net/?f=%5Csin%5E2%7B4x%7D%3D%5Cfrac%7B1%7D%7B4%7D%3B%7C%5Csin%7B4x%7D%7C%3D%5Cfrac%7B1%7D%7B2%7D%5C%5C%5Csin%7B4x%7D%3D%D0%B1%5Cfrac%7B1%7D%7B2%7D)
4x=±π/6+πn, n∈Z.
Ответ: x=±π/24+πn/4, n∈Z.
2)![\cos^2{\frac{x}{5} }=\frac{3}{4} ;\cos{\frac{x}{5} }=б\frac{\sqrt{3} }{2} \cos^2{\frac{x}{5} }=\frac{3}{4} ;\cos{\frac{x}{5} }=б\frac{\sqrt{3} }{2}](https://tex.z-dn.net/?f=%5Ccos%5E2%7B%5Cfrac%7Bx%7D%7B5%7D%20%7D%3D%5Cfrac%7B3%7D%7B4%7D%20%3B%5Ccos%7B%5Cfrac%7Bx%7D%7B5%7D%20%7D%3D%D0%B1%5Cfrac%7B%5Csqrt%7B3%7D%20%7D%7B2%7D)
x/5=±π/6+πn, n∈Z.
Ответ: x=±5π/6+5πn, n∈Z.
3)![12\sin^2{x}-5=0;\sin{x}=б\sqrt{\frac{5}{12}}=б\frac{\sqrt{15} }{6} 12\sin^2{x}-5=0;\sin{x}=б\sqrt{\frac{5}{12}}=б\frac{\sqrt{15} }{6}](https://tex.z-dn.net/?f=12%5Csin%5E2%7Bx%7D-5%3D0%3B%5Csin%7Bx%7D%3D%D0%B1%5Csqrt%7B%5Cfrac%7B5%7D%7B12%7D%7D%3D%D0%B1%5Cfrac%7B%5Csqrt%7B15%7D%20%7D%7B6%7D)
Ответ: x=±arcsin(√15/6)+πn, n∈Z.