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<p class="Cell">The number of integral values of k for which the equation <img src="data:image/png;base64,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" class="Wirisformula" alt="7 cos space x plus 5 sin space x equals 2 k plus 1" width="180" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»7«/mn»«mi»cos«/mi»«mo»§#160;«/mo»«mi»x«/mi»«mo»+«/mo»«mn»5«/mn»«mi»sin«/mi»«mo»§#160;«/mo»«mi»x«/mi»«mo»=«/mo»«mn»2«/mn»«mi»k«/mi»«mo»+«/mo»«mn»1«/mn»«/math»'/>has a solution is

Solution for the question - the number of integral values of k for which the equation 7cos x+5sinx=2k+1 has a solution is 121084