Question

Assertion :The period of $f\left(x\right)=2\cos \frac{1}{3}(x-\pi )+4\sin \frac{1}{3}(x-\pi )$ is $3\pi$ Reason: If $T$ is the period of $f\left(x\right)$, then the period $f(ax+b)$ is $\frac{T}{|a|}$

• 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. Both Assertion and Reason are incorrect

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

$f\left(x\right)=2\cos \frac{1}{3}(x-\pi )+4\sin \frac{1}{3}(x-\pi )$

We know that Period of $a\cos x+b\sin x$ is

$2\pi$ where $a\ne b$

So Period $a\cos (cx+d)+b\sin (cx+d)$ is

$\frac{2\pi }{|c|}$

$\begin{array}{cc}\text{Period of}f\left(x\right)\text{is}& 2\pi \left(3\right)=6\pi \end{array}$

If $T$ is the period of $f\left(x\right)$ then perid $f(ax+h)$ is $\frac{\pi }{|a|}$

Assertion is incorrect and reason is correct