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

Using the identity $(a+b)^2=a^2+2ab+b^2$, we can expand the given expression as 
$$\sin^2(\omega)+2\sin(\omega)\cos(\omega)+\cos^2(\omega).$$
Using the identity $\sin^2(\omega)+\cos^2(\omega)=1$, we can simplify the expression as 
$$\sin^2(\omega)+2\sin(\omega)\cos(\omega)+\cos^2(\omega)=1+2\sin(\omega)\cos(\omega).$$ 
Thus, the correct answer is (C).

Expand the Expression Below and Use Fundamental Trigonometric Identities to Simplify