Question

The period of the function $f\left(x\right)=cose{c}^2\left(3x\right)+cot\left(4x\right)$ is:

• A. $\frac{\mathrm{\pi }}{3}$
• B. $\frac{\mathrm{\pi }}{3}$
• C. $\frac{\mathrm{\pi }}{6}$
• D. $\mathrm{\pi }$

Answer 1

The correct option is D

$\mathrm{\pi }$

Explanation for the correct option:

Compute the period of the given function.

$f\left(x\right)=cose{c}^2\left(3x\right)+cot\left(4x\right)$

We know that the period of $\cos e{c}^{2}x$ is $\mathrm{\pi }$ .

Thus, the period of $\cos e{c}^2\left(3x\right)$ is $\frac{\mathrm{\pi }}{3}$.

Also, we know that the period of $cot\left(x\right)$ is $\mathrm{\pi }$ .

Thus, the period of $cot\left(4x\right)$ is $\frac{\mathrm{\pi }}{4}$.

Now, we need to calculate the LCM of $\left(\frac{\mathrm{\pi }}{3},\frac{\mathrm{\pi }}{4}\right)$ , which is given as:

$\frac{\mathrm{LCM}\mathrm{of}\mathrm{numerators}}{\mathrm{HCF}\mathrm{of}\mathrm{denominators}}$

$$\begin{gathered} =\frac{\pi }{1} \\ =\pi \end{gathered}$$

Thus, the period of $f\left(x\right)=cose{c}^2\left(3x\right)+cot\left(4x\right)$ is $\mathrm{\pi }$.

Hence, Option$\left(\mathrm{D}\right)$ is the correct answer