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

Question

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

Quizplus · Accepted Answer

Expanding $(\sin x - \cos x)^2$ gives $\sin^2 x - 2\sin x\cos x + \cos^2 x$. Using the Pythagorean identity $\sin^2 x + \cos^2 x = 1$, this simplifies to $1 - 2\sin x\cos x$.

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 $( \sin x - \cos x ) ^ { 2 }$