Question

The number of integral values of $K$, for which the equation $7\cos x+5\sin x=2K+1$ has a solution, is

• A. 4
• B. 8
• C. 10
• D. 12

Answer 1

Answer: (B)

$-\sqrt{7^2+5^2}\le (7\cos x+5\sin x)\le \sqrt{7^2+5^2}$
So, for solution, $-\sqrt{74}\le (2K+1)\le \sqrt{74}$
$\Rightarrow -8.6\le (2K+1)\le 8.6$
$\Rightarrow -9.6\le 2K\le 7.6$
$\Rightarrow -4.8\le K\le 3.8$
So, integral values of $K$ are
$-4,-3,-2,-1,0,1,2,3$ (eight values)