SOLUTION: Graph the expression sec2 x - sec2 x sin2 x on your calculator. Determine what constant or single function is equivalent to the given expression.

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Question 641426: Graph the expression sec2 x - sec2 x sin2 x on your calculator. Determine what constant or single function is equivalent to the given expression.

Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
sec˛x - sec˛x·sin˛x

To put that in your calculator

(1/cos(x))˛-(1/cos(x))˛(sin(x))˛

To graph that on a TI-83 or 84, don't press GRAPH, 
but instead press ZOOM, then press 7


Factor out sec˛x

sec˛x(1 - sin˛x)

Use the identity: cos˛x + sin˛x = 1 and solve for cos˛x
                          cos˛x = 1 - sin˛x
So replace 1 - sin˛x by cos˛x

sec˛x(cos˛x)

Then replace sec˛x by 1%2Fcos%5E2%28x%29

(cos˛x)·1%2Fcos%5E2%28x%29 =

%28cos%5E2%28x%29%29%2F%28cos%5E2%28x%29%29 =

           1 

The constant 1.  However, sec˛x - sec˛x·sin˛x is not defined
as 1 or as any number at all when x = any odd multiple of 90°
if you're using degrees or pi%2F2 if you're using radians.                

Edwin