# trig identities help needed

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• Sep 4th 2010, 06:11 PM
link0099
trig identities help needed
so i have my end of prelims coming up and doing a revision test. this question came up

$\displaystyle prove (sec^2x - 1)cos^2x = sin^2x$
Now i thought that you would do the question like this:

$\displaystyle LHS = (sec^2x-1)cos^2x = (Tan^2x)cos^2x = \frac{\sin^2x}{cos^2x} cos^2x =sin^2x$

but it gave a different soln. am i wrong?
• Sep 4th 2010, 06:21 PM
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Quote:

Originally Posted by link0099
so i have my end of prelims coming up and doing a revision test. this question came up

$\displaystyle prove (sec^2x - 1)cos^2x = sin^2x$
Now i thought that you would do the question like this:

$\displaystyle LHS = (sec^2x-1)cos^2x = (Tan^2x)cos^2x = \frac{\sin^2x}{cos^2x} cos^2x =sin^2x$

but it gave a different soln. am i wrong?

Your proof is valid. The book most likely uses $\displaystyle \sin^2x+\cos^2x=1$ which of course if you divide through by $\displaystyle \cos^2x$ gives the identity you used.
• Sep 4th 2010, 06:42 PM
link0099
oh good, thanks a lot