Question

encontrar la identidad trigonometríca
ayudame porfis ​

Answer 1

Explicación paso a paso:

$(1 - \cos {}^{2} a)(1 + \cot {}^{2} (a) ) = 1 \\ (1 - \cos {}^{2} (a) )(1 + \frac{ \cos {}^{2} (a) }{ \sin {}^{2} (a) } ) = 1 \\ (1 - \cos {}^{2} (a) )( \frac{ \sin {}^{2} (a) + \cos {}^{2} (a) }{ \sin {}^{2} (a) } ) = 1$

Sabemos que sen^2 a +cos^2 a = 1, por lo que sen^2 = 1 - cos^2 a y cos ^2 = 1 - sen ^2 a

Entonces sustituimos en la identidad nuestra

$\sin {}^{2} (a) ( \frac{1}{ \sin {}^{2} (a) } ) = 1 \\ \frac{ \sin {}^{2} (a) }{ \sin {}^{2} (a) } = 1 \\ 1 = 1$