# How to simplify #cos^2 2theta-sin^2 2theta#?

This is basically the double angle formula

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This simplifies to

Hopefully this helps!

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You can simplify ( \cos^2(2\theta) - \sin^2(2\theta) ) using the double angle identities for cosine and sine:

( \cos(2\theta) = \cos^2(\theta) - \sin^2(\theta) ) ( \sin(2\theta) = 2\sin(\theta)\cos(\theta) )

Applying these identities:

( \cos^2(2\theta) - \sin^2(2\theta) = \cos^2(2\theta) - (1 - \cos^2(2\theta)) )

Then, expand and simplify:

( \cos^2(2\theta) - (1 - \cos^2(2\theta)) = \cos^2(2\theta) - 1 + \cos^2(2\theta) )

Combine like terms:

( \cos^2(2\theta) + \cos^2(2\theta) - 1 )

( 2\cos^2(2\theta) - 1 )

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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