Question

If $\left[si{n}^{-1}x\right]+\left[co{s}^{-1}x\right]=0;x\in [0,\infty );$ the solution set for x is

• A. $(cos1,1)$
• B. $(-1,cos1)$
• C. $(sin1,1)$
• D. $(cos1,sin1)$

Answer 1

Answer: (D)

$(cos1,sin1)$

$\left[{\sin }^{-1}x\right]+\left[{\cos }^{-1}x\right]=0x\in [0,\infty ]$

If $x$ is positive than

when $x=\cos 1$ to $0$

$\left[{\cos }^{-1}x\right]$ is $1$

and when $x=\sin 1$ to $0$

$\left[{\sin }^{-1}x\right]$ is $1$

but we want both as zero

so $x\in (\cos 1,\sin 1)$

$D$ is correct.