Question

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Answer 1

Step-by-step explanation:

We have,

$\rm \: \cos(x) + \sin \bigg( \frac{3\pi}{2} + x \bigg) - \sin \bigg( \frac{3\pi}{2} - x \bigg) + \cos(\pi + x)$

$\rm \: = \cos(x) - \cos( x ) - ( - \cos ( x )) - \cos( x)$

$\rm \: = \cos(x) - \cos( x ) + \cos ( x ) - \cos( x)$

$\rm \: = 0$