Solve this: Use the following information to answer the next question A function is said - Maths - Trigonometric Functions

Question

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
f(-x)=-f(x)

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

Neha Sethi · Accepted Answer

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
Regards