Example 12

Example 12 rutor of •lexive. again m The period of tan x is n so perirud of tan (2n + 3) W2. If fix) = Isin xl then + = Isin (x + Isin = fix). Thus the period offis r. Example 12: Which of the following functions is an function (c) y = cosx Ans. (d) r of 2. 6 40 O Solution: If fix) = — 2r2 thenfl—x) — x' - 2r: = Ax). Hence fis an even function. If u(x) = x ad -x) = x — so u is neither even nor an odd functi cos x. A—x) cos(—x) = cos x = p(x) so p is e 6 40 6 41

Dear Student,
Please find below the solution to the asked query:

A function is odd function if f-x=-fxafx=x4-2x2f-x=-x4-2-x2=x4-2x2=fxf-x-fxHence fx=x4-2x2 is not odd function.bfx=x-x2f-x=-x--x2=-x-x2=-x+x2f-x-fxHence fx=x-x2 is not odd function.cfx=cosxf-x=cos-x=cosx=fxf-x-fxHence fx=cosx is not odd function.dfx=x-x36+x540f-x=-x--x36+-x540=-x+x36-x540=-x-x36+x540=-fxf-x=-fxHence fx=x-x36+x540 is an odd function.Hence optiond is correct.

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