Question

The number of solutions $\left[\cos x\right]+\left|\sin x\right|=1$ in $\pi \le x<3\pi$, where $\left[x\right]$ is the greatest integer not exceeding $x$ is

• A. $3$
• B. $4$
• C. $2$
• D. $1$

Answer 1

Answer: (A)

$3$

We first plotted the graph of $\sin x$ and $\cos x$

Then using the properties of integral part and mode function we get the graph of $\left[\cos x\right]$ and $\left|\sin x\right|$

Clearly they collectively give $1$ at $x=\frac{3\pi }{2},2\pi ,\frac{5\pi }{2}$ in the interval $[\pi ,3\pi ]$

So option $A$ is correct