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Question

The number of integral values of k for which the equation 7cosx+5sinx=2k+1 has a solution is

A
8
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B
9
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C
10
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D
12
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Solution

The correct option is A 8
7cosx+5sinx=2k+1
This is acosx+bsinx=c form.
So, solution is possible iff
1ca2+b2112k+172+521742k+1741742k1+742k=4,3,2,1,0,1,2,3

Hence, there are 8 integral values of k.

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