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How do you use the double angle formula to rewrite #5-10sin^2x#?

Answer 1

Brooklyn Anderson

Think about (list) double angle formulas until you come to one that looks useful.

#sin(2 theta) = 2sin theta cos theta# Doesn't look helpful

#cos(2 theta) = cos^2 theta - sin^2 theta# -- Hmmmm, probably not but there are other forms for this one

#cos(2 theta) = 1 - 2sin^2 theta#. Compare this to what we started with.

If I factored out a 5, I'd have:

#5-10sin^2x = 5(1-2sin^2x)# and that's just

#5cos(2x)#

So there it is.

#5-10sin^2x = 5cos(2x)#

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Answer 2

Violet Anderson

To rewrite (5 - 10\sin^2(x)) using the double angle formula, follow these steps:

Recognize that (\sin^2(x) = \frac{1 - \cos(2x)}{2}), which is the double angle formula for sine squared.
Substitute (\sin^2(x)) with (\frac{1 - \cos(2x)}{2}) in the expression (5 - 10\sin^2(x)).
Simplify the expression to get the final result.

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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.