Question

comprobar la siguiente identidad trigonométrica

tan 3t. 1 - cos3t
-------------- = --------------
1+cos 3t. Sen 3t cos 3t​

Answer 1

Para comprobar la identidad trigonométrica dada por:

$\frac{tg(3t)}{1+con(3t)}=\frac{1-cos(3t)}{sin(3t)*cos(3t)}$

Procedemos de la forma siguiente:

$tg(3t)*sin(3t)*cos(3t)=[1+con(3t)]*[1-cos(3t)]$

$\frac{sin(3t)*sin(3t)*cos(3t)}{cos(3t)}=1 -cos(3t)+cos(3t)-cos^2(3t)$

$sin^2(3t)=1-cos^2(3t)$

$sin^2(3t)+cos^2(3t)=1$

$1 = 1$

Queda demostrada la identidad trigonométrica:

$\frac{tg(3t)}{1+con(3t)}=\frac{1-cos(3t)}{sin(3t)*cos(3t)}$