Convert the expression.
$( 2 \sin x + 2 \cos x ) ^ { 2 }$
A) $4 - 4 \sin 2 x$
B) $2 + 4 \sin x$
C) $4 + 4 \sin x$
D) $4 - 4 \sin x$
E) $4 + 4 \sin 2 x$

Question

Convert the expression.  
  $( 2 \sin x + 2 \cos x ) ^ { 2 }$  
A)  $4 - 4 \sin 2 x$
B)  $2 + 4 \sin x$
C)  $4 + 4 \sin x$
D)  $4 - 4 \sin x$
E)  $4 + 4 \sin 2 x$

Quizplus · Accepted Answer

Expanding the given expression using the identity $(a + b)^2 = a^2 + 2ab + b^2$, we get $4\sin^2x + 4\sin x\cos x + 4\cos^2x$. Simplifying further using the Pythagorean identity $\sin^2x + \cos^2x = 1$ and the double angle formula $\sin 2x = 2\sin x\cos x$, we obtain $4 + 4\sin 2x$.

Convert the Expression (2sin⁡x+2cos⁡x)2( 2 \sin x + 2 \cos x ) ^ { 2 }(2sinx+2cosx)2

Convert the Expression $( 2 \sin x + 2 \cos x ) ^ { 2 }$