1.

Iflog_("sin"(pi)/(4)) sin x gt 0 , x in [ 0. 4pi). Themfind the region of x satisfying the inequality .

Answer»

Solution :We have ,
` log_("sin"(pi)/(4)) sin x gt 0 `
`rArr log_((1)/(sqrt(2))) sin x gt 0 `
` rArr (sin x ) LT ((1)/(sqrt(2)))^(0) as 0 lt (1)/(sqrt(2)) lt 1`
`rArr (sin x) lt 1 "but sin" x gt 0 `
` rArr 0 lt sin x lt 1 `
`rArr x in (,(pi)/(2)) cup((pi)/(2) , pi)cup(2pi, (5pi)/(2)) cup ((5pi)/(2) ,3pi)`.


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