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JEE Advanced

Exam: JEE Advanced
Subject: Mathematics
Chapter: Trigonometry

JEE Advanced · Mathematics · Trigonometry

If [ x ] represents the greatest integer less than or equal to x ,...

If [ x ] represents the greatest integer less than or equal to

x

, then which of the following statement is true

Options

A $\sin [x]=\cos [x]$ has no solution
B $\sin [x]=\tan [x]$ has infinitely many solutions
C $\sin [x]=\cos [x]$ possess unique solution
D $\sin [x]=\tan [x]$ for no value of $x$

Correct answer

B. $\sin [x]=\tan [x]$ has infinitely many solutions

Step-by-step solution

Since, according to option

(\mathrm{A})

, we have

\begin{aligned} & \sin [x]=\cos [x] \\ & \Rightarrow[x]=n \pi+\left(\frac{\pi}{4}\right)=\left(n+\frac{1}{4}\right) \pi \end{aligned}

Which is not possible, as LHS

\in I

and

R H S \in Q^{{}^{{}^{\circ}}}

Hence,

\sin [x]=\cos [x]

has no solution However,

\sin [\mathrm{x}]=\tan [\mathrm{x}]\Rightarrow[\mathrm{x}]=\mathrm{n} \pi, \mathrm{n} \in \mathrm{I}

Which is possible when

[x]=0

and

n=0\therefore 0 \leq \mathrm{x} \lt 1

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