Question

Usando las Identidades Fundamentales, comprobar: Sen²u(1+cot²u)=1 ​

Answer 1

Recuerda:

$\sin {}^{2} (x) + \cos {}^{2} (x) = 1$

$\cot(x) = \frac{ \cos(x) }{ \sin(x) }$

...

$\sin {}^{2} (u) (1 + \cot {}^{2} (u)) = 1 \\ \sin {}^{2} (u) + \sin {}^{2} (u) \times \cot {}^{2} (u) = 1 \\ \sin {}^{2} (u) + \sin {}^{2} (u) \times \frac{ \cos {}^{2} (u) }{ \sin {}^{2} (u) } = 1 \\ \sin {}^{2} (u) + \cos {}^{2} (u) = 1 \\ 1 = 1$