Esercizio
$\cos^2a+\cos^2b+\cos^2c\:=\:1$
Soluzione passo-passo
Impara online a risolvere i problemi di differenziazione logaritmica passo dopo passo. cos(a)^2+cos(b)^2cos(c)^2=1. Applicare la formula: x+a=b\to x=b-a, dove a=\cos\left(b\right)^2+\cos\left(c\right)^2, b=1, x+a=b=\cos\left(a\right)^2+\cos\left(b\right)^2+\cos\left(c\right)^2=1, x=\cos\left(a\right)^2 e x+a=\cos\left(a\right)^2+\cos\left(b\right)^2+\cos\left(c\right)^2. Applicare la formula: -\left(a+b\right)=-a-b, dove a=\cos\left(b\right)^2, b=\cos\left(c\right)^2, -1.0=-1 e a+b=\cos\left(b\right)^2+\cos\left(c\right)^2. Applying the trigonometric identity: 1-\cos\left(\theta \right)^2 = \sin\left(\theta \right)^2. Applicare la formula: x^a=b\to \left(x^a\right)^{\frac{1}{a}}=\pm b^{\frac{1}{a}}, dove a=2, b=\sin\left(b\right)^2-\cos\left(c\right)^2 e x=\cos\left(a\right).
cos(a)^2+cos(b)^2cos(c)^2=1
Risposta finale al problema
$a=\arccos\left(\sqrt{\sin\left(b\right)^2-\cos\left(c\right)^2}\right),\:a=\arccos\left(-\sqrt{\sin\left(b\right)^2-\cos\left(c\right)^2}\right)$