Easy trig simplification problem.

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September 4th 2009, 09:21 AM
kdickson91

Easy trig simplification problem.

I know this problem is very easy, I am just having so much trouble grasping the concept. I have to verify this problem and don't know where to start.http://i16.photobucket.com/albums/b4...27/problem.jpg
Any help GREATLY appreciated. Homework due at 3PM today. :(
September 4th 2009, 02:15 PM
DavidEriksson

We know that $\sec t=\frac{1}{\cos t}$ , $\csc t=\frac{1}{\sin t}$ and $\cos^2 t + \sin^2 t =1$ so starting with the LHS:
LHS $=\frac{\sec t}{\cos t}-\frac{\sec^2 t}{\csc^2 t}=\frac{\frac{1}{\cos t}}{\cos t}-\frac{\frac{1}{\cos^2 t}}{\frac{1}{\sin^2 t}}=\frac{1}{\cos^2 t}-\frac{\sin^2 t}{\cos^2 t} =\frac{1-\sin^2 t}{\cos^2 t}=\frac{\cos^2 t}{\cos^2 t}=1=$ RHS

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