Question

Perform the multiplication and use the fundamental identities to simplify. There is more than one correct form of the answer.(4 sin x + 4 cos x)^2

Answer 1

Simplify the given expression as shown below

`\begin{gathered} (4sinx+4cosx)^2=(4(sinx+cosx))^2=16(sinx+cosx)^2=16(sin^2x+2sinxcosx+cos^2x) \\ =16(1+2sinxcosx) \\ =16+32sinxcosx \end{gathered}`

And, in general,

`\begin{gathered} sin(2x)=2sinxcosx \\ \Rightarrow16+32sinxcosx=16+16sin(2x) \end{gathered}`

The simplified answer is 16+16sin(2x)