Question

Graph the expression sec^2 x - sec^2 x sin^2 x on your calculator. Determine what constant or single function is equivalent to the given expression.

Answer 1

You can graph this and if the problem requires you to then you will have to do so, but the answer can be gotten much quicker by realizing that sec^2 times sin^2 is sin^2 over cos^2 which is tan^2. Now you have the identity:

sec^2 - tan^2 = 1

So, you will always have "1".

Answer 2

thank you!

Answer 3

This identity comes from

sec^2 - (sec^2)(sin^2) = (sec^2)(1 - sin^2) = (sec^2)(cos^2)

= (cos^2)/(cos^2) = 1

Answer 4

One more thing, though.

Answer 5

okay..

Answer 6

You have to realize that your original expression has a sec in it, so it is undefined at pi/2 and 3pi/2 or pi/2 + kpi. Don't forget the "0" in denominator rule!

Answer 7

oh okay thank ya!

Answer 8

You're welcome!