# How do you prove #(sinx+cosx)^2 = 1+2sinxcosx#?

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#### Explanation

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Use trigonometric identities and the FOIL method.

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We are asked to prove that

1) Change

2) Utilize the FOIL method for multiplying binomials, e.g.

3) Simplify and group like terms:

4) Recall the trigonometric identity which states

5) Use substitution:

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