Question

Which of the following option is incorrect?
$(n\in Z)$

• A. $\cos \left[\frac{(2n+1)\pi }{2}\right]=0$
• B. $\cos \left(2n\pi \right)=1$
• C. $\cos \left[\right(2n+1\left)\pi \right]=-1$
• D. $\cos \left(n\pi \right)=1$

Answer 1

The correct option is D $\cos \left(n\pi \right)=1$

Checking all be given options, putting $n=0$, we get
$\cos \left[\frac{(2n+1)\pi }{2}\right]=\cos \frac{\pi }{2}=0\cos \left(2n\pi \right)=\cos 0=1\cos \left[\right(2n+1\left)\pi \right]=\cos \pi =-1\cos \left(n\pi \right)=\cos 0=1$

Checking all be given options, putting $n=1$, we get
$\cos \left[\frac{(2n+1)\pi }{2}\right]=\cos \frac{3\pi }{2}=0\cos \left(2n\pi \right)=\cos 2\pi =1\cos \left[\right(2n+1\left)\pi \right]=\cos 3\pi =-1\cos \left(n\pi \right)=\cos \pi =-1$

So, $\cos \left(n\pi \right)=\pm 1$