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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

Perform the multiplication and use the fundamental identities to simplify There is more than one correct form of the answer4 sin x 4 cos x2 class=

Respuesta :

Simplify the given expression as shown below

[tex]\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}[/tex]

And, in general,

[tex]\begin{gathered} sin(2x)=2sinxcosx \\ \Rightarrow16+32sinxcosx=16+16sin(2x) \end{gathered}[/tex]

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

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