Solve this:

Use the following information to answer the next question. 

A function is said to be an even function if f (-x) = f (x) and odd function if 

Which of the following trigonometric functions is neither an odd function nor an even function? 
(A) sin x + cos x
(B) cos x + tan2x
(C) cot x + cosec x
(D) (tan x + cot x) x cosec x

Dear student
Even function: f-x=fx  ...1Odd function:  f-x=-fx  ...2Consider , option ALet fx=sinx+cosxThen  f-x=sin-x+cos-x=-sinx+cosxIt is not satisfying either of 1 or 2So, it is neither an even function nor odd.Consider , option BLet fx=cosx+tan2xThen  f-x=cos-x+tan2-x=cosx+tan-x×tan-x=cosx+-tanx×-tanx=cosx+tan2x=fxSo, f is an even function.Similarly you can try others.Note:tan-x=-tanxcos-x=cosxsin-x=-sinx

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