Question

arcctg(4x-1)=arcsin 1 (найдите x)

Answer 1

$arcctg(4x-1)=arcsin1\\arcctg(4x-1)=frac{pi}{2}\\ctgBig (arcctg(4x-1)Big )=ctgfrac{pi}{2}\\star ; ; ctg(arcctg alpha )= alpha ; ,; esli; ; -infty textless alpha textless +infty; ; star \\4x-1=ctgfrac{pi}{2}\\4x-1=0\\4x=1\\x=frac{1}{4}$