The number of integral values of k, for which | vedclass

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Question

(b) $ - \sqrt {{7^2} + {5^2}} \le (7\cos x + 5\sin x) \le \sqrt {{7^2} + {5^2}} $
So, for solution $ - \sqrt {74} \le (2k + 1) \le \sqrt {74} $
or $

Vedclass · Accepted Answer

$8$

Vedclass · Answer

(b) $ - \sqrt {{7^2} + {5^2}} \le (7\cos x + 5\sin x) \le \sqrt {{7^2} + {5^2}} $
So, for solution $ - \sqrt {74} \le (2k + 1) \le \sqrt {74} $
or $ - 8.6 \le (2k + 1) \le 8.6$ or $ - 9.6 \le 2k \le 7.6$
or $ - 4.8 \le k \le 3.8.$ So, integral values of k are $ - 4,\, - 3,\, - 2,\, - 1,\,0,\,1,\,2,\,3$ $(eight\, values).$

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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