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3.4.2: Identidades de Doble Ángulo
https://espanol.libretexts.org/Educacion_Basica/Trigonometria/03%3A_Identidades_trigonom%C3%A9tricas/3.04%3A_Identidades_de_%C3%A1ngulo_doble_y_medio/3.4.02%3A_Identidades_de_Doble_%C3%81ngulo
\(\begin{aligned} \sin 2x+\cos 3x &=2\sin x\cos x+\cos (2x+x) \\&=2\sin x\cos x+\cos 2x\cos x−\sin 2x\sin x \\&=2\sin x\cos x+(\cos ^2x−\sin ^2x)\cos x−(2\sin x\cos x)\sin x \\ &=2\sin x\cos x+\cos ^3... $\begin{aligned} \sin 2x+\cos 3x &=2\sin x\cos x+\cos (2x+x) \\&=2\sin x\cos x+\cos 2x\cos x−\sin 2x\sin x \\&=2\sin x\cos x+(\cos ^2x−\sin ^2x)\cos x−(2\sin x\cos x)\sin x \\ &=2\sin x\cos x+\cos ^3x−\sin ^2x\cos x−2\sin ^2x\cos x \\ &=2\sin x\cos x+\cos ^3x−3\sin ^2x\cos x \end{aligned}$ $\begin{aligned}\sin ^4x−\cos ^4x&=(\sin ^2x−\cos ^2x)(\sin ^2x+\cos ^2x)\\&=−(\cos ^2x−\sin ^2x)\\&=−\cos ^2x \end{aligned}$
7.3: Identidades de ángulo doble
https://espanol.libretexts.org/Matematicas/Precalculo_y_Trigonometria/Libro%3A_Prec%C3%A1lculo_-_Una_investigaci%C3%B3n_de_funciones_(Lippman_y_Rasmussen)/07%3A_Ecuaciones_trigonom%C3%A9tricas_e_identidades/7.03%3A_Identidades_de_%C3%A1ngulo_doble
\[\begin{array}{l} {\sin ^{2} (\alpha )=\dfrac{1-\cos (2\alpha )}{2} } \\ {\sin (\alpha )=\pm \sqrt{\dfrac{1-\cos (2\alpha )}{2} } } \\ {\alpha =\dfrac{\theta }{2} } \\ {\sin \left(\dfrac{\theta }{2} ... $\begin{array}{l} {\sin ^{2} (\alpha )=\dfrac{1-\cos (2\alpha )}{2} } \\ {\sin (\alpha )=\pm \sqrt{\dfrac{1-\cos (2\alpha )}{2} } } \\ {\alpha =\dfrac{\theta }{2} } \\ {\sin \left(\dfrac{\theta }{2} \right)=\pm \sqrt{\dfrac{1-\cos \left(2\left(\dfrac{\theta }{2} \right)\right)}{2} } } \\ {\sin \left(\dfrac{\theta }{2} \right)=\pm \sqrt{\dfrac{1-\cos (\theta )}{2} } } \end{array}\nonumber$

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