Answers

2014-01-28T01:56:46+08:00
(sin x + cos x)^4 = (1 + 2sinxcosx)²
Find the square root of both sides,
(sin x + cos x)² = 1 + 2sinxcosx
by expanding LHS,
sin²x + 2sinxcosx + cos²x = 1 + 2sinxcosx
By the Pythagorean Identity sin²x + cos²x = 1 and substituting it to the LHS, we get:

1 + 2sinxcosx = 1 + 2sinxcosx

Thus, proving the identity.
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