Question

Demostrar la siguiente identidad trigonometría
1/cscx-cotx=cotx+cscx

Answer 1

1/[csc(x)-ctg(x)]=

1/[(1/sen(x))-(cos(x)/sen(x))]=

1/[(1-cos(x))/sen(x)]=

1× sen(x)/(1-cos(x))=

sen(x)/[1-cos(x)]



ctg(x)+csc(x)=

Cos(x)/sen(x)+ 1/sen(x)=

[cos(x)+1]/sen(x)



sen(x)/[1-cos(x)]=[cos(x)+1]/sen(x)

sen²(x)/[(1-cos(x))(1+cos(x))=1

sen²(x)/[1-cos²(x)]=1

sen²(x)/sen²(x)=1

1=1