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What is the maximum value of 3 sin 2x + 4 cos 2x?
- A3
- B4
- C5
- D1
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CCommunity
3 sin 2x + 4 cos 2x
$(= \;3{\sin ^2}{\rm{x\;}} + {\rm{\;}}4 - 4{\sin ^2}{\rm{x\;}} = {\rm{\;}}4 - {\sin ^2}{\rm{x}})$ (cos 2x = 1 - sin 2x)
Now we want to find maximum value of the above expression so minimum value of
$(\begin{array}{l}
{\sin ^2}{\rm{x\;}} = {\rm{\;}}0\\
4 - {\sin ^2}{\rm{x\;}} = {\rm{\;}}4 - 0{\rm{\;}} = {\rm{\;}}4
\end{array})$
$(= \;3{\sin ^2}{\rm{x\;}} + {\rm{\;}}4 - 4{\sin ^2}{\rm{x\;}} = {\rm{\;}}4 - {\sin ^2}{\rm{x}})$ (cos 2x = 1 - sin 2x)
Now we want to find maximum value of the above expression so minimum value of
$(\begin{array}{l}
{\sin ^2}{\rm{x\;}} = {\rm{\;}}0\\
4 - {\sin ^2}{\rm{x\;}} = {\rm{\;}}4 - 0{\rm{\;}} = {\rm{\;}}4
\end{array})$