How do you simplify ${(sin θ - cos θ)}^{2}$ $(sin theta - cos theta)^2$ ?

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Answer 1 · 2016-04-12T23:09:58

Let's multiply!

$(sin θ - cos θ) (sin θ - cos θ)$ $(sin theta - costheta)(sin theta - costheta)$

${sin}^{2} θ - cos θ sin θ - cos θ sin θ + {cos}^{2} θ$ $sin^2theta - costhetasintheta - costhetasintheta + cos^2theta$

Applying the pythagorean identity ${sin}^{2} θ + {cos}^{2} θ = 1$ $sin^2theta + cos^2theta = 1$ :'

$1 - 2 cos θ sin θ$ $1 - 2costhetasintheta$

How do you simplify (sinθ−cosθ)2(sin theta - cos theta)^2?