The number of integral values of k, for which the equation 7 $c o s x + 5 s i n x = 2 k + 1$ has a solution, is

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Solution

The correct option is B 8
$- \sqrt{7^{2} + 5^{2}} \leq (7 c o s x + 5 s i n x) \leq \sqrt{7^{2} + 5^{2}}$
So, for solution $- \sqrt{74} \leq (2 k + 1) \leq \sqrt{74}$
or $- 8.6 \leq (2 k + 1) \leq 8.6 o r - 9.6 \leq 2 k \leq 7.6$
or $- 4.8 \leq k \leq 3.8$ , So, integral values of k are -4, -3, -2, -1, 0, 1, 2, 3 (eight values)

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