How do you multiply and simplify ${(sin x - cos x)}^{2}$ $(sinx-cosx)^2$ ?

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Answer 1 · 2016-11-18T18:19:42

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

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

Using the pattern:

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

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

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

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

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

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