Math  /  Trigonometry

Questionsin(7π2+α)+cos(6πα)+tan(7π2+α)cos(3π2α)+sin2(π2+α)+sin2(α)\sin \left(\frac{7 \pi}{2}+\alpha\right)+\cos (6 \pi-\alpha)+\tan \left(\frac{7 \pi}{2}+\alpha\right) \cos \left(\frac{3 \pi}{2}-\alpha\right)+\sin ^{2}\left(\frac{\pi}{2}+\alpha\right)+\sin ^{2}(-\alpha)

Studdy Solution
Sommare tutti i termini semplificati:
cos(α)+cos(α)1+cos2(α)+sin2(α)-\cos(\alpha) + \cos(\alpha) - 1 + \cos^2(\alpha) + \sin^2(\alpha)
Osserviamo che cos(α)+cos(α)=0-\cos(\alpha) + \cos(\alpha) = 0 e cos2(α)+sin2(α)=1\cos^2(\alpha) + \sin^2(\alpha) = 1.
Quindi, l'espressione totale diventa:
01+1=00 - 1 + 1 = 0

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