The number of integral values of m for which the equation Sin x -3cos x -4 m -6-4- m has solutions is

2 ≤4m 6/4 m≤ 2 ⇒ m ϵ [ 1, 7/3 ] ⇒ m = 1, 0, 1, 2 ...

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The number of integral values of m for which the equation $S i n x - \sqrt{3} c o s x = \frac{4 m - 6}{4 - m}$ has solutions is ___

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The number of integral values of $m$ for which the equation $s i n x - \sqrt{3} c o s x = \frac{4 m - 6}{4 - m}$ has solution is:

sin x - \sqrt{3} cos x = \frac{4 m - 6}{4 - m}

x ϵ [0, 2 π]

sin x - \sqrt{3} cos x = \frac{4 m - 6}{4 - m}

x \in [0, π]

Possible integral value(s) of m for the equation $s i n x - \sqrt{3} c o s x = \frac{4 m - 6}{4 - m}$ can be valid for some $x ϵ [0, 2 π]$ , is

x ϵ [0, 4 π]

∣ \sqrt{3} cos x - sin x ∣\geq 2

∣ c o s (x + π / 6) ∣= 1 \Rightarrow

∣ \sqrt{3} cos x - sin x ∣\geq 2

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