<p><strong>Trigonometric Functions</strong></p>
<p>In the table below, \(A, B\) are constants, and \(C\) is an arbitrary constant.</p>
<div class="content-block content-block--table"><div class="table-container"><table><caption>Trigonometric functions: \(\sin, \cos, \tan, \sec, \mathrm{cosec} \)</caption><thead><tr style="height: 40px;"><th style="height: 40px; min-height: 40px; text-align: left; --cell-justify: flex-start">Differentiation</th><th style="height: 40px; min-height: 40px; text-align: left; --cell-justify: flex-start">Integration</th></tr></thead><tbody><tr style="height: 40px;"><td style="height: 40px; min-height: 40px; text-align: left; --cell-justify: flex-start">\(\frac{\mathrm{d}}{\mathrm{d}x}\sin(Ax+B) = A\cos(Ax+B)\)</td><td style="height: 40px; min-height: 40px; text-align: left; --cell-justify: flex-start"><p>\(\displaystyle \int \cos(Ax+B) \, \mathrm{d}x = \frac{1}{A}\sin(Ax+B) + C\)</p></td></tr><tr style="height: 40px;"><td style="height: 40px; min-height: 40px; text-align: left; --cell-justify: flex-start">\(\frac{\mathrm{d}}{\mathrm{d}x}\cos(Ax+B) = -A\sin(Ax+B)\)</td><td style="height: 40px; min-height: 40px; text-align: left; --cell-justify: flex-start"><p>\(\displaystyle  \int \sin(Ax+B) \, \mathrm{d}x = -\frac{1}{A}\cos(Ax+B) + C\)</p></td></tr><tr style="height: 40px;"><td style="height: 40px; min-height: 40px; text-align: left; --cell-justify: flex-start"><p>\(\frac{\mathrm{d}}{\mathrm{d}x}\tan(Ax+B) = A\sec^{2}(Ax+B)\)</p></td><td style="height: 40px; min-height: 40px; text-align: left; --cell-justify: flex-start"><p>\(\displaystyle \int \sec^{2}(Ax+B) \, \mathrm{d}x = \frac{1}{A}\tan(Ax+B) + C\)</p></td></tr><tr style="height: 40px;"><td style="height: 40px; min-height: 40px; text-align: left; --cell-justify: flex-start">\(\frac{\mathrm{d}}{\mathrm{d}x}\sec(Ax+B) = A\sec(Ax+B)\tan(Ax+B)\)</td><td style="height: 40px; min-height: 40px; text-align: left; --cell-justify: flex-start"><p>\(\displaystyle  \int \sec(Ax+B)\tan(Ax+B) \, \mathrm{d}x = \frac{1}{A}\sec(Ax+B) + C\)</p></td></tr><tr style="height: 40px;"><td style="height: 40px; min-height: 40px; text-align: left; --cell-justify: flex-start">\(\frac{\mathrm{d}}{\mathrm{d}x}\mathrm{cosec}(Ax+B) = -A\mathrm{cosec}(Ax+B)\cot(Ax+B)\)</td><td style="height: 40px; min-height: 40px; text-align: left; --cell-justify: flex-start"><p>\(\displaystyle \int \mathrm{cosec}(Ax+B)\cot(Ax+B) \, \mathrm{d}x = \) </p><p>\( -\frac{1}{A}\mathrm{cosec}(Ax+B) + C\)</p></td></tr><tr style="height: 40px;"><td style="height: 40px; min-height: 40px; text-align: left; --cell-justify: flex-start"><p>\(\frac{\mathrm{d}}{\mathrm{d}x}\cot(Ax+B) = -A\mathrm{cosec}^{2}(Ax+B)\)</p></td><td style="height: 40px; min-height: 40px; text-align: left; --cell-justify: flex-start"><p>\(\displaystyle  \int \mathrm{cosec}^{2}(Ax+B) \, \mathrm{d}x = -\frac{1}{A}\cot(Ax+B) + C\)</p></td></tr></tbody></table></div></div>

In the table below, \(A, B\) are constants, and \(C\) is an arbitrary constant.

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