trigonometry - Will this Trigonometric give the following answer?

If $n$ is an integer, can $$\cos[(2n-1)\pi/2]-\cos[(2n-1)\pi/4]$$

be equal to $\;\;\cos[(2n-1)\pi/4],\;\;?$

I have tried the formula for $\cos A-\cos B$ but that would give result in $sine$

Answer

Hint: $$\cos \left((2n-1)\frac{\pi}{2}\right)=\cos \left(\pi n-\frac{\pi}{2}\right)=0.$$