A) 4
B) 8
C) 10
D) 12
Correct Answer: B
Solution :
[b]| We have, \[7\cos x+5\sin x=2k+1\] |
| The minimum and maximum value of \[7\cos x+5\sin x\] is \[-\sqrt{{{7}^{2}}+{{5}^{2}}},\sqrt{{{7}^{2}}+{{5}^{2}}}\],\[-\sqrt{74},\sqrt{74}\] |
| \[\therefore \]\[-\sqrt{74}<2k+1<\sqrt{74}\] |
| \[\Rightarrow \]\[-\,8<2k+1<8\] |
| \[\Rightarrow \]\[-\,4\le k\le 3\] |
| \[k=-\,4,-\,3,-\,2,-1,0,1,2,3\] |
| Total 8 integral value. |
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