Use fundamental identities to simplify the expression below and then determine which of the following is not equivalent.
A)
B)
C)
D)

Question

Use fundamental identities to simplify the expression below and then determine which of the following is not equivalent. 
A)​ 
B)​ 
C)​ 
D)​

Quizplus · Accepted Answer

Using the fundamental identity $\sin^2 x + \cos^2 x = 1$, we can simplify the expression as $11\cos^2(	heta)\sin^2(	heta)$. Then, using the double angle formula $\sin(2x) = 2\sin(x)\cos(x)$, we can simplify further as $11\cdot\frac{1}{2}\sin(2	heta)\cdot\frac{1}{2}\cos(2	heta) = \frac{11}{4}\sin(2	heta)\cos(2	heta)$. 
Comparing this with the answer choices, we see that only option D is not equivalent, as it has a different value for $\sin(2	heta)\cos(2	heta)$.

Use Fundamental Identities to Simplify the Expression Below and Then