# Verifying a trig identity

• Aug 9th 2013, 11:45 AM
curt26
Verifying a trig identity
I have

1/sin^2(t) + 1/cos^2(t) = 1/sin^2(t)-sin^4(t)

I started on the right side of the identity and got to this stage:

1/sin^2(t) + 1/1-sin^2(t)

On the left side of the identity I got to this stage:

1/sin^2(t)(1-sin^2(t))

I know I need to go farther on the right side of the identity but I am stuck at this point. Any help would be great thanks!
• Aug 9th 2013, 12:19 PM
$\frac{1}{sin^2(t)}+\frac{1}{1-sin^2(t)}=\frac{1-sin^2(t)+sin^2(t)}{sin^2(t)[1-sin^2(t)]}=\frac{1}{sin^2(t)-sin^4(t)}$