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

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Solution

The correct option is B
8

Since $- \sqrt{a^{2} + b^{2}} \leq a s i n x + b c o s x \leq \sqrt{a 62 + b^{2}}$

$∴ - \sqrt{74} \leq 7 c o s x + 5 s i n x \leq \sqrt{74}$

So $- \sqrt{74} < 2 K + 1 < \sqrt{74}$

Therefore 2K + 1 = ±8 , ±7 , ±6 ............ , ± 1 , 0

So K = -1 , ±3 , ±2 , ±1,0

So 8 values of K .

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