Aprende con Inteligencia

Resolver el sistema:
$$ \begin{cases} \sin x \cos 2y = a^2 + 1 \\ \cos x \sin 2y = a \end{cases} $$

Resolver la siguiente ecuación:
$$ \arcsin \left( \tan \frac{\pi}{4} \right) - \arcsin \sqrt{\frac{3}{x}} - \frac{\pi}{6} = 0 $$

Compruebe la siguiente igualdad:
$$ \tan 30^\circ + \tan 40^\circ + \tan 50^\circ + \tan 60^\circ = \frac{8 \sqrt{3} \cos 20^\circ}{3} $$

Resolver la ecuación:
$$ 3 \arccos x - \pi x - \frac{\pi}{2} = 0 $$

Halle los valores de las siguientes funciones trigonométricas:

1. [(i)] $\sin(135^\circ)$
2. [(ii)] $\cos(150^\circ)$
3. [(iii)] $\tan(120^\circ)$
4. [(iv)] $\sin(225^\circ)$
5. [(v)] $\sec(240^\circ)$
6. [(vi)] $\tan(300^\circ)$
7. [(vii)] $\sin(330^\circ)$
8. [(viii)] $\tan(315^\circ)$
9. [(ix)] $\cos(315^\circ)$
10. [(x)] $\sin(405^\circ)$

Sea $f: (-1, 1) \to R$ tal que $f(\cos 4\theta) = \frac{2}{2 - \sec^2 \theta}$ para $\theta \in \left( 0, \frac{\pi}{4} \right) \cup \left( \frac{\pi}{4}, \frac{\pi}{2} \right)$. Entonces los valores de $f\left(\frac{1}{3}\right)$ son:
(a) $1 - \sqrt{\frac{3}{2}}$
(b) $1 + \sqrt{\frac{3}{2}}$
(c) $1 - \sqrt{\frac{2}{3}}$
(d) $1 + \sqrt{\frac{2}{3}}$

Resolver el sistema:
$$ \begin{cases} \cos^2 4x + \frac{\sqrt{26}-2}{2} \tan(-2y) = \frac{\sqrt{26}-1}{4} \\ \tan^2 (-2y) - \frac{\sqrt{26}-2}{2} \cos 4x = \frac{\sqrt{26}-1}{4} \end{cases} $$

Paso 1:
1435. $\sin 4x \cos x \tan 2x = 0$

Simplificar la expresión:
$$ \cos \left( \frac{1}{2} \arccos x \right) $$

Demuestre que:
$$ (\cos \alpha + \sin \beta)^2 + (\sin \alpha - \cos \beta)^2 = 4 \cos^2 \left( 45^\circ + \frac{\alpha - \beta}{2} \right) $$

Resolver la ecuación:
$$ 4x^4 + x^6 = -\sin^2 5x $$

Demuestre que:
$$ \cos(2x + 2y) = \cos 2x \cos 2y + \cos^2 (x + y) - \cos^2 (x - y) $$