Question

$sin( \frac{pi}{2}+x)sinx+cos( \frac{pi}{2} +x)coxs$

Answer 1

   
[tex]\displaystyle \\ \sin\Big( \frac{\pi}{2}+x\Big)\sin x+\cos\Big( \frac{\pi}{2} +x\Big)\cos x = \\ \\ -\cos x\cdot \sin x + \sin x \cdot \cos x = \\ \\ \sin x ~\cos x - \sin x~ \cos x = \boxed {0} [/tex]