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If sin x + cos x=K+1, then find all the ...

If `sin x + cos x=K+1`, then find all the integral values of K.

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Verified by Experts

As,
`-sqrt(2) le sin x + cos x le sqrt(2)`
`-sqrt(2) le K + 1 le sqrt(2)`.
`-sqrt(2) -1 le K le sqrt(2)-1`
Hence integral values of K are `-2,-1,0`. Total 3 values exist.
`-1 le sin(x+pi/4) le 1`
Maximum value occurs when `x+pi/4 =pi/2`.
`x=pi/4`
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