Expand the expression below and use fundamental trigonometric identities to simplify. $$( \sin ( \omega ) + \cos ( \omega ) ) ^ { 2 }$$
A) $\sin ^ { 2 } ( \omega ) + \cos ^ { 2 } ( \omega )$
B) $2 \tan ( \omega ) + 1$
C) $2 \sin ( \omega ) \cos ( \omega ) + 1$
D) 1
E) $2 \cot ( \omega ) + 1$

Question

Quizplus · Accepted Answer

Expanding $( \sin ( \omega ) + \cos ( \omega ) ) ^ { 2 }$ gives $\sin^2(\omega) + 2\sin(\omega)\cos(\omega) + \cos^2(\omega)$. Using the Pythagorean identity $\sin^2(\omega) + \cos^2(\omega) = 1$, this simplifies to $1 + 2\sin(\omega)\cos(\omega)$, which matches option C.

Expand the Expression Below and Use Fundamental Trigonometric Identities to Simplify