Number of integral values of k $7\cos x+5\sin x=2k+1$ for which the equation  has solution

$We have -\sqrt{a^2+b^2}\le a\cos \theta +b\sin \theta \le \sqrt{a^2+b^2}$

$\Rightarrow -\sqrt{74}\le 7\cos x+5\sin x\le \sqrt{74}$

$\Rightarrow -\sqrt{74}\le 2k+1\le \sqrt{74}$

$\Rightarrow k=-4,-3,-2,-1,0,1,2,3$