Question

If $lo{g}_{\frac{1}{\sqrt{2}}}sinx>0,xϵ[0,4\pi ]$ then the number of values of x which are integral multiples of $\frac{\pi }{4}$ is

• A. 4
• B. 12
• C. 3
• D. None of these

Answer 1

The correct option is A 4

$0<\frac{1}{\sqrt{2}}<1$


$lo{g}_{\frac{1}{\sqrt{2}}}sinx>0,xϵ[0,4\pi ]\Rightarrow 0<sinx<1$
$\therefore$ Integral multiple of $\frac{\pi }{4}$ will be
$\frac{\pi }{4},\frac{3\pi }{4},\frac{9\pi }{4},\frac{11\pi }{4}$
Number of required values = 4.