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)#