SOLUTION: Hello, I've been working on this problem for about an hour and I'm having a very hard time understanding this trigonometric identity question: Write the first expression in term

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Question 1141807: Hello, I've been working on this problem for about an hour and I'm having a very hard time understanding this trigonometric identity question:
Write the first expression in terms of the second if the terminal point determined by (t) is in the given quadrant.
(sec^2(t))(sin^2(t)), cos(t); any quadrant
Basically, I need to show (sec^2(t))(sin^2(t)) in terms of cos(t) and 1.
I know that sec^2(t) = tan^2(t) + 1 and that sin^2(t) = 1 - cos^2(t), but I get confused when I have to start converting the squared Pythagorean identities into the Basic trigonometric identities as I don't know what gets square-rooted and what the equations change into.
Answer by greenestamps(13367) (Show Source):
You can put this solution on YOUR website!

The second part of what you say you know is useful, because it writes the sin^2(t) in terms of cos(t).

The first part of what you say you know doesn't help, because it writes sec^2(t) in terms of tan^2(t).

You want to do the same thing with the sec^2(t) that you did with the sin^2(t) -- write it in terms of cos(t).

So... what is the relationship between sec(t) and cos(t)?