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Question

If y=sin nx+cos nx (x, n real), then 2y2

A
True
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B
False
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Solution

The correct option is A True
We have
y=sin nx+cos nx
=2[1(2)sin nx+1(2)cos nx]
=2[cos π4sin nx+sin π4cos nx]
=2sin(nx+π4)
Since 1sin(nx+π4)1
we have 22sin(nx+π4)2
that is 2y2

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