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[tex]sin( \frac{pi}{2}+x)sinx+cos( \frac{pi}{2} +x)coxs[/tex]

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[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]



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