Răspuns:
[tex]\sin \bigg(\dfrac{\pi}{2} - x\bigg) = \sin \dfrac{\pi}{2} \cos x - \cos \dfrac{\pi}{2} \sin x = 1 \cdot \cos x - 0 \cdot \sin x = \cos x[/tex]
[tex]\cos \bigg(\dfrac{\pi}{2} - x\bigg) = \cos \dfrac{\pi}{2} \cos x + \sin \dfrac{\pi}{2} \sin x = 0 \cdot \cos x - 1 \cdot \sin x = - \sin x[/tex]
Așadar:
[tex]\sin \bigg(\dfrac{\pi}{2} - x\bigg) - \cos \bigg(\dfrac{\pi}{2} - x\bigg) = \cos x - \sin x[/tex]
Formule utilizate:
[tex]\boxed{\boldsymbol{ \sin (\alpha - \beta) = \sin \alpha \cos \beta - \cos \alpha \sin \beta }}[/tex]
[tex]\boxed{\boldsymbol{ \cos (\alpha - \beta) = \cos \alpha \cos \beta + \sin \alpha \sin \beta }}[/tex]
