Confused about notation of $\sin^2 \theta$

Here's a snippet from the working in a trigonometry textbook. I'm confused about the second line:

Am I correct in interpreting from this that: $1 - \sin^2 \theta \equiv (1 - \sin\theta)^2$ ?

Until now I had thought that $1 - \sin^2 \theta \equiv 1 - (\sin\theta)^2$

Which is correct?

Thanks!

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1 Answer

I think your eyes skipped the "-" in the second expression.

$$(a + b) (a - b) = a^2 - b^2$$

And so:

$$1 - \sin^2 \theta = (1 + \sin \theta) (1 - \sin \theta)$$

$1 - \sin^2 \theta = 1 - (\sin \theta)^2$ is correct.

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Ah of course, thank you! Difference of two squares. I must have misread the second line as you said. –  Danny King Apr 4 '11 at 15:11