If log1-2 sin x - 0- x - -0- 4 - then the number of values of x which are integral multiples of -4 is

0 lt; 1/√(2) lt; 1 log_1/√(2) sin x gt; 0, x ϵ [0, 4 π] ⇒ 0 lt; sin x lt; 1 ∴ Integral multiple of π/4 will be π/4, 3 π/4, 9 π/4, 11 π/4 Number ...

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Properties of Inequalities

If log1/√2 si...

Question

If $l o g_{\frac{1}{\sqrt{2}}} s i n x > 0, x ϵ [0, 4 π]$ then the number of values of x which are integral multiples of $\frac{π}{4}$ is

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

\frac{π}{4}

{log}_{\frac{1}{\sqrt{2}}} sin x \geq 0

x \in [0, 4 π]

x

\frac{π}{4}

{log}_{1 / \sqrt{2}} sin x > 0, x \in [0, 4 π],

x

\frac{π}{4},

f : [0, 4 π] \to [0, π]

f (x) = c o s^{- 1} (c o s x)

x ϵ [0, 4 π]

f (x) = \frac{10 - x}{10}

f (x) = ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ \begin{matrix} x + a^{2} \sqrt{2} s i n x, & 0 \leq x < \frac{π}{4} x c o t x + b, & \frac{π}{4} \leq x < \frac{π}{2} b s i n 2 x - a c o s 2 x, & \frac{π}{2} \leq x \leq π \end{matrix}

[0, π]

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