How do you simplify $(sin theta + cos theta) ^2$ ?

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Answer 1 · 2015-10-18T20:04:21

$(sin(theta) +cos(theta))^2 = sin(2theta) + 1$

$(sin(theta) +cos(theta))^2 = sin^2(theta) + 2sin(theta)cos(theta) + cos^2(theta)$

We know that $sin^2(theta) + cos^2(theta) = 1$ so

$(sin(theta) +cos(theta))^2 = 2sin(theta)cos(theta) + 1$

However, $2sin(theta)cos(theta) = sin(2theta)$ so we can say

$(sin(theta) +cos(theta))^2 = sin(2theta) + 1$

How do you simplify (sin theta + cos theta) ^2 (sin theta + cos theta) ^2 ?