Question

Assertion :Fundamental period of $\cos x+\cot x$ is $2\pi$. Reason: If the period of $f\left(x\right)$ is $T_1$ and the period of $g\left(x\right)$ is $T_2$, then the fundamental period of $f\left(x\right)+g\left(x\right)$ is the L.C.M. of $T_1$ and $T_2$.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Answer 1

The correct option is C Assertion is correct but Reason is incorrect

$f\left(x\right)=cosx+cotx$
$=h\left(x\right)+g\left(x\right)$ where $h\left(x\right)=cos\left(x\right)$ and $g\left(x\right)=cot\left(x\right)$.
Now fundamental period of $cos\left(x\right)$ is $2\pi$ and fundamental period of $cot\left(x\right)$ is $\pi$.
Therefore the fundamental period of $f\left(x\right)$ will be $2\pi$.

Reason is incorrect since it is not applicable for every function.