The number of solutions of equation [sin x ] = [1 + sin x] + [ 1 - cos x] where [.] denotes the greatest integer function and is

1 solution

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2 solutions

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3 solutions

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No solution

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Solution

The correct option is D
No solution

[sin x ] = [1 + sin x ] + [1 - cos x]

$\Rightarrow$ 0 = 2 + [- cosx]

$\Rightarrow$ [-cosx] = -2

Since -1 $\leq$ cos $\leq$ 1 $\Rightarrow$ [-cosx] $\neq$ -2

Hence no solution

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Similar questions

[sin x] = cos x \forall x \in [0, 2 π]

[]

[y + [y]] = 2 cos x

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[sin x + cos x] = 3 + [- sin x] + [- cos x]

[0, 2 π]

[.]

[cos x] + | sin x | = 1

π \leq x \leq 3 π

[.]

| . |

sin x = [x]

.

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