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Find the number of integral values of k ...

Find the number of integral values of k for which the equation `7 cos x+5 sin x=2k+1` has at least one solution.

A

4

B

8

C

10

D

12

Text Solution

Verified by Experts

The correct Answer is:
b
We know that,
` -sqrt (a ^(2) + b ^(2) ) le a sin x + b cos x le sqrt(a^(2) + b ^(2))`
` therefore - sqrt (74) le 7 cos x + 5 sin x le sqrt ( 74)`
i.e ` " " - sqrt( 74) le 2k + 1 le sqrt (74) `
Since, k is integer, ` - 9 lt 2k + 1 lt 9`
` rArr - 10 lt 2k lt 8 rArr - 5 ly k lt 4`.
` rArr ` Number of possible integer values of `k = 8`.
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