SOLUTION: Perform the multiplication and use fundamental identities to simplify: (sin x + cos x)^2

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Question 105526This question is from textbook Precalculus with limits
: Perform the multiplication and use fundamental identities to simplify:
(sin x + cos x)^2This question is from textbook Precalculus with limits

Answer by Fombitz(13828) About Me  (Show Source):
You can put this solution on YOUR website!
(sin x + cos x)^2
Using the FOIL Method,
%28sin+x+%2B+cos+x%29%5E2=sin%5E2%28x%29%2B2cos%28x%29sin%28x%29%2Bcos%5E2%28x%29 FOIL method.
You know the following trig identity,
sin%5E2%28x%29%2Bcos%5E2%28x%29=1
Substitute that in your equation,
%28sin+x+%2B+cos+x%29%5E2=1%2B2cos%28x%29sin%28x%29
Another indentity (fundamental identity, I think) is,
sin%282x%29=2sin%28x%29cos%28x%29
Substitute that into your equation,
%28sin+x+%2B+cos+x%29%5E2=1%2B2cos%28x%29sin%28x%29
%28sin+x+%2B+cos+x%29%5E2=1%2Bsin%282x%29