If y+cos⁡θ=sin⁡θ has a real solution then

If $y + \cos θ = \sin θ$ has a real solution then

A
$- \sqrt{2} \leq y \leq \sqrt{2}$
B
$y > \sqrt{2}$
C
$y \leq - \sqrt{2}$
D
none of these

Solution:

We have $y = \sin θ - \cos θ$ and $\sin θ - \cos θ$

lies between $- \sqrt{2}$ and $+ \sqrt{2}$

$∴ - \sqrt{2} \leq y \leq \sqrt{2} .$

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