Complete the identity.
-$( \sin x + \cos x ) ^ { 2 } =$ ?
A) $1 + \sin 2 x$
B) $\sin 2 x$
C) $1 - \cos 2 x$
D) $1 + \cos 2 x$

Question

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 $\sin^2 x + \cos^2 x = 1$ and the double angle formula for sine $\sin 2x = 2\sin x \cos x$, the expression simplifies to $1 + \sin 2x$.

Complete the Identity (sin⁡x+cos⁡x)2=( \sin x + \cos x ) ^ { 2 } =(sinx+cosx)2=

Complete the Identity $( \sin x + \cos x ) ^ { 2 } =$