How do you multiply and simplify $(sinx-cosx)^2$ ?

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Answer 1 · 2016-11-18T18:19:42

Use the pattern $(a - b)^2 = a^2 - 2ab + b^2$ and then simplify:

$(sin(x) - cos(x))^2 = 1 - sin(2x)$

Using the pattern:

$(sin(x) - cos(x))^2 = sin^2(x) - 2sin(x)cos(x) + cos^2(x)$

Use the identity $sin^2(x) + cos^2(x) = 1$

$(sin(x) - cos(x))^2 = 1 - 2sin(x)cos(x)$

Use the identity $sin(2x) = 2sin(x)cos(x)$

$(sin(x) - cos(x))^2 = 1 - sin(2x)$

How do you multiply and simplify (sinx-cosx)^2(sinx-cosx)^2?