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

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Correct answer: C. (c) Let f (x )=7 cos ⁡x+5 sin ⁡x=2k+1 Maximum and minimum value of f (x )=7 cos ⁡x+5 sin ⁡x is 49+25 ,- 49+25 ⇒ 74 ,- 74 ∴- 74 2k+1 74 ∵k is an integer value. ⇒-8 2k+1 8 ⇒-9 2k 7 ⇒- 92 k 72 ∴k= -4 ,-3 ,-2 ,-1 ,0 ,1 ,2 ,3 Total number of values of k=8.

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

Solution

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