# How do you prove : #Sin4x - cos4x + 1 = 2Sin2x#?

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To prove the identity ( \sin^4 x - \cos^4 x + 1 = 2\sin^2 x ):

- Start with the left-hand side (LHS) of the equation: ( \sin^4 x - \cos^4 x + 1 ).
- Use the trigonometric identity ( \sin^2 x + \cos^2 x = 1 ) to replace ( \sin^2 x ) or ( \cos^2 x ) wherever appropriate.
- Express ( \sin^4 x ) and ( \cos^4 x ) in terms of ( \sin^2 x ) using the identity ( \sin^2 x = 1 - \cos^2 x ) and ( \cos^2 x = 1 - \sin^2 x ).
- Simplify the expression until it equals the right-hand side (RHS) of the equation: ( 2\sin^2 x ).

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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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