# trig identities help needed

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

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

$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?
• September 4th 2010, 06:21 PM
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Quote:

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

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

$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 $\sin^2x+\cos^2x=1$ which of course if you divide through by $\cos^2x$ gives the identity you used.
• September 4th 2010, 06:42 PM