Can you please help me simplify #(sin(x) + cos(x))^2#?

1 Answer
Douglas K.
Mar 9, 2018

Given: #(sin(x) + cos(x))^2#

Expand the square:

#(sin(x) + cos(x))^2 = sin^2(x) + 2sin(x)cos(x) + cos^2(x)#

Substitute #sin^2(x) + cos^2(x) = 1#:

#(sin(x) + cos(x))^2 = 2sin(x)cos(x) + 1#

Substitute #2sin(x)cos(x) = sin(2x)#

#(sin(x) + cos(x))^2 = sin(2x) + 1#

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