Posted by **Melody** on Sunday, January 3, 2010 at 6:01pm.

Are any of these three problems identities?

1. Cos^2x-sin^2x=1-2sin^2x

2. Sinxsecx=cosxcscx

3. Sec^4x-tan^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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