Let $$f(x)=2x(sinx+tanx)2x+21$$ππ−$$41$$,x≠nπ, then f is (where$$ [ . ] represents greatest integer $$function)

Correct option is 1an odd function

Questions

Let $f (x) = \frac{2 x (\sin x + \tan x)}{2 [\frac{x + 21 π}{π}] - 41}, x \neq n π$ , then f is (where [ . ] represents greatest integer function)

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an odd function

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detailed solution

Correct option is A

The denominator is=2x+21ππ−41=2xπ+21−41=221+xπ−41=2xπ+1∴ f(x)=x(sinx+tanx)xπ+12⇒f(−x)=−xsin(−x)+tan(−x)−xπ+12=x(sinx+tanx)−1−xπ+12=−x(sinx+tanx)xπ+12=−f(x)

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Let f(x)=2x(sinx+tanx)2x+21ππ−41,x≠nπ, then f is (where [ . ] represents greatest integer function)

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Let $f (x) = \frac{2 x (\sin x + \tan x)}{2 [\frac{x + 21 π}{π}] - 41}, x \neq n π$ , then f is (where [ . ] represents greatest integer function)