If l o g 1 √ 2 s i n x > 0 , x ϵ [ 0 , 4 π ] then the number of values of x which are integral multiples of π 4 is Options: A . &nbsp4 B . &nbsp12 C . &nbsp3 D . &nbspNone of these

Answer: Option A : A 0 < 1 √ 2 < 1 l o g 1 √ 2 s i n x > 0 , x ϵ [ 0 , 4 π ] ⇒ 0 < s i n x < 1 ∴ Integral multiple of π 4 will be π 4 , 3 π 4 , 9 π 4 , 11 π 4 Number of required values = 4.

If log1√2sin x>0,xϵ[0,4π] then the number of values of x which are integ

Question

l o g_{\frac{1}{\sqrt{2}}} s i n x > 0, x ϵ [0, 4 π]

then the number of values of x which are integral multiples of

\frac{π}{4}

Options:

A . 4

B . 12

C . 3

D . None of these

Answer: Option A
:
A

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

If Log1√2sin x>0,xϵ[0,4π] Then The Number Of Values ...

l o g_{\frac{1}{\sqrt{2}}} s i n x > 0, x ϵ [0, 4 π] \Rightarrow 0 < s i n x < 1

∴

Integral multiple of

\frac{π}{4}

will be

\frac{π}{4}, \frac{3 π}{4}, \frac{9 π}{4}, \frac{11 π}{4}

Number of required values = 4.

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