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Simplify the following expression, if possible.
Leave your answer in terms of [tex]\(\sin(\theta)\)[/tex] and [tex]\(\cos(\theta)\)[/tex].

[tex]\[
(\sin(\theta) - \cos(\theta))^2 = \square
\][/tex]

Sagot :

GinnyAnswer
Sure, let's simplify the given expression [tex]\((\sin(\theta) - \cos(\theta))^2\)[/tex].

Here’s the step-by-step solution:

1. Expand the Expression:
[tex]\[ (\sin(\theta) - \cos(\theta))^2 \][/tex]

We use the algebraic identity for the square of a binomial: [tex]\((a - b)^2 = a^2 - 2ab + b^2\)[/tex]. In this case, [tex]\(a = \sin(\theta)\)[/tex] and [tex]\(b = \cos(\theta)\)[/tex].

2. Apply the Identity:
[tex]\[ (\sin(\theta) - \cos(\theta))^2 = \sin(\theta)^2 - 2\sin(\theta)\cos(\theta) + \cos(\theta)^2 \][/tex]

3. Combine Like Terms:
[tex]\[ \sin(\theta)^2 - 2\sin(\theta)\cos(\theta) + \cos(\theta)^2 \][/tex]

So, the simplified expression is:
[tex]\[ \sin(\theta)^2 - 2\sin(\theta)\cos(\theta) + \cos(\theta)^2 \][/tex]
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