Question

Statement 1: $f\left(x\right)=\cos (x^2-\tan x)$ is a non-periodic function
Statement 2: $x^2-\tan x$ is a non-periodic function

• A. Both the statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1
• B. Both the statements are TRUE and STATEMENT 2 is NOT the correct explanation of STATEMENT 1
• C. STATEMENT 1 is TRUE and STATEMENT 2 is FALSE
• D. STATEMENT 1 is FALSE and STATEMENT 2 is TRUE

Answer 1

The correct option is B Both the statements are TRUE and STATEMENT 2 is NOT the correct explanation of STATEMENT 1

The following graph of $y=cos(x^2-tanx)$ shows that f(x) is a non periodic function.
This is due to the fact that there exists no T such that $f\left(x\right)=f(x+T)$.
Also $f\left(x\right)\ne f(-x)$ in the above case.
$f\left(x\right)=cos(x^2-tanx)$
$f(-x)=cos(x^2+tanx)$. Hence it is neither even nor odd.
And $f\left(x\right)=x^2-tanx$ is a non-periodic function and neither odd nor even function as $x^2$ is even function and tan(x) is an odd function.