Question

Statement 1: Period of ${\sin }^{3}x+{\cos }^{3}x$ is $2\pi$
Statement 2: Period of $\sin \left(\frac{x}{n}\right)$ is $4\pi \Rightarrow n=2$

• A. only I is true
• B. only II is true
• C. Both I and II are true
• D. Neither I nor II true

Answer 1

Answer: (C)

Both I and II are true

We've the period of the functions $\sin x$ and $\cos x$ is $2\pi$.

Also the period of the function ${\sin }^{3}x$ and ${\cos }^{3}x$ is $2\pi$.

And hence the period of the function ${\sin }^{3}x+{\cos }^{3}x$ is $2\pi$.

So statement-I is true.

Now the period of the function $\sin \frac{x}{n}$ is $2\pi n$.

According to the problem we have,

$2\pi n=4\pi$

Or, $n=2$.

So statement-II is also true.