Question

Possible integral value(s) of m for the equation $sinx-\sqrt{3}cosx=\frac{4m-6}{4-m}$ can be valid for some $xϵ[0,2\pi ]$, is

• A. -1
• B. 0
• C. 1
• D. 2

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A

-1

B

0

C

1

D

2

$-2\le sinx-\sqrt{3}cosx\le 2$

Hence $-2\le \frac{4m-6}{4-m}\le 2$

$-1\le \frac{2m-3}{4-m}\le 1$

now if $\frac{2m-3}{4-m}\le 1$

$\frac{(2m-3)-(4-m)}{4-m}\le 0$

$\frac{3m-7}{m-4}\ge 0$

Again $-1\le \frac{2m-3}{4-m}$ or $\frac{(2m-3)+(4-m)}{4-m}\ge 0$

$\frac{m+1}{m-4}\le 0$

hence m $ϵ[-1,\frac{7}{3}]\Rightarrow mϵ\{-1,0,1,2\}$