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The number of integral values of k for ...

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

A

4

B

8

C

10

D

12

Text Solution

Verified by Experts

The correct Answer is:
B
We know that maximum and minimum value of `7cosx+5sinx " are "sqrt(7^(2)+5^(2))and-sqrt(7^(2)+5^(2)) " i.e"sqrt(74)and-sqrt(74)`.
`because7cosx+5sinx " lie in " [-sqrt(74),sqrt(74)]`
`therefore-sqrt(74)lt2k+1ltsqrt(74)`
`rArrk=0,+-1,+-2,+-3,-4`
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