Find number of solutions to the equation:
$[sin x + cos x] = 3 + [- sin x] + [- cos x]$

0

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1

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2

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infinite

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Solution

The correct option is A $0$
$[s i n x + c o s x] = 3 + [- s i n x] + [- c o s x]$
$- \sqrt{2} \leq s i n x + c o s x \leq \sqrt{2}$
$∴$ $[s i n x + c o s x]$ can be $- 2, - 1, 0, 1$
$- 1 \leq s i n x \leq 1$
$∴$ $[s i n x]$ can be $- 1, 0, 1$
$- 1 \leq c o s x \leq 1$
$∴$ $[c o s x]$ can be $- 1, 0, 1$
But no value of $x$ can satisfy the equation as simultaneous values of $x$ make it impossible.

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