Perform the multiplication and use the fundamental identities to simplify.
$( \sin x + \cos x ) ^ { 2 }$
A) $1 + \sin x + \cos x$
B) $1 + \sin x \cos x$
C) $1 + 2 \sin x + \cos x$
D) $1 + 2 \sin x \cos x$
E) $2 + 2 \sin x \cos x$

Question

Perform the multiplication and use the fundamental identities to simplify. 
$( \sin x + \cos x ) ^ { 2 }$ 
A) $1 + \sin x + \cos x$
B) $1 + \sin x \cos x$
C) $1 + 2 \sin x + \cos x$
D) $1 + 2 \sin x \cos x$
E) $2 + 2 \sin x \cos x$

Quizplus · Accepted Answer

Expanding the square gives:
$$(\sin x + \cos x)^2 = \sin^2 x + 2\sin x \cos x+ \cos^2 x$$
Using the identity $\sin^2 x + \cos^2 x = 1$, we can simplify further:
$$(\sin x + \cos x)^2 = 1 + 2\sin x \cos x$$
Therefore, the answer is D, $1+2\sin x \cos x$.

Perform the Multiplication and Use the Fundamental Identities to Simplify (sin⁡x+cos⁡x)2( \sin x + \cos x ) ^ { 2 }(sinx+cosx)2

Perform the Multiplication and Use the Fundamental Identities to Simplify $( \sin x + \cos x ) ^ { 2 }$