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

Answer 1

Aaliyah Abdullah

The question seems to have been written incorrectly.

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Answer 2

Daniel Acosta

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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Answer from HIX Tutor

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.