The correct option is B 8
To find the number of integral values of k, for which the equation
7cosx+5sinx=2k+1
As we know that , maximum value of 7cosx+5sinx is
=√72+52
=√74=8.6
Minimum value of 7cosx+5sinx is
=−√72+52
=−8.6
So, the value will vary between −8.6 and 8.6
Since 2k+1 is an odd integer
Odd integer between −8.6 and 8.6 is
−7,,−5,−3,−1,1,3,5,7
and corresponding value of k will be
−4,−3,−2,−1,0,1,2,3
Hence, there are 8 values of k