The number of solution of $\left|cosx\right|$  = sinx, such that   $-4\pi \le x\le 4\pi is:$

<p>Number of solution of the equation |cos x| = sin x for <span contenteditable="false"> <math> <mrow> <mi>x</mi> <mo>∈</mo> <mrow> <mo> [</mo> <mrow> <mo>−</mo> <mn>4</mn> <mi>π</mi> <mo>, </mo> <mn>4</mn> <mi>π</mi> </mrow> <mo>]</mo> </mrow> </mrow> </math> </span><math><mrow><mrow><mrow></mrow></mrow></mrow></math>&nbsp;will be equal to 4 times the number of solutions of the same equation for <span contenteditable="false"> <math> <mrow> <mi>x</mi> <mo>∈</mo> <mrow> <mo> [</mo> <mrow> <mn>0</mn> <mo>, </mo> <mn>2</mn> <mi>π</mi> </mrow> <mo>]</mo> </mrow> </mrow> </math> </span><math><mrow><mrow><mrow></mrow></mrow></mrow></math></p><p>Graphs of y = |cos x| and y = sin x are as shown below.</p><p><img ></p><p>Hence, two solutions of given equation in [0, 2]</p><p><math></math><span contenteditable="false"> <math> <mrow> <mo>⇒</mo> </mrow> </math> </span>&nbsp;total of 8 solutions in [4, 4]</p>

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