Posted by Melody on Sunday, January 3, 2010 at 6:01pm.
Are any of these three problems identities?
1. Cos^2xsin^2x=12sin^2x
2. Sinxsecx=cosxcscx
3. Sec^4xtan^4/sec^2x=1+sin^2x
If so, how can you conclude that any of them are identities?

Trig  Marth, Sunday, January 3, 2010 at 6:24pm
Yes. You can prove an identity by rearranging one side of the equation to match the other.
For example:
1.
cos^2(x)  sin^2(x) = 1  sin^2(x)  sin^2(x) because cos^2(x) + sin^2(x) = 1
= 1  2 sin^2(x)

Trig  MathMate, Sunday, January 3, 2010 at 8:39pm
The second one is not an identity. You can prove this by substituting the appropriate sin/cos functions for sec(x) and csc(x).
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