Question

1)3cos10x–8cos5x+5=0
2)Промежуток [π/6,π/2]
Объясните 2часть поподробней

Answer 1

1)
$3cos10x-8cos5x+5=0\6cos^25x-8cos5x+2=0\2(cos5x-1)(3cos5x-1)=0\\x={2pi kover5},kin Z\x={pm arccos{1over3}+2pi kover5},kin Z$

2)
${0piover5} textless {piover6} textless {2piover5} textless {piover2} textless {4piover5}\\arccos{1over3} textless {piover6}\\{arccos{1over3}over5} textless {piover6} textless {2piover5}-{piover30} textless {2piover5}-{arccos{1over3}over5}} textless {arccos{1over3}over5}+{2piover5} textless \ textless {piover30}+{2piover5} textless {piover2} textless {4piover5}-{piover30} textless {4piover5}-{arccos{1over3}over5}\\xin{{2piover5},{2piover5}-{arccos{1over3}over5},{2piover5}+{arccos{1over3}over5}}$