Question:

<p><strong>Step 1:</strong> Rewrite the expression:</p><p>$3 \csc 20° - \sec 20° = \frac{3}{\sin 20°} - \frac{1}{\cos 20°}$</p><p><strong>Step 2:</strong> Combine fractions:</p><p>$= \frac{3\cos 20° - \sin 20°}{\sin 20° \cos 20°}$</p><p><strong>Step 3:</strong> Factor the numerator:</p><p>$= \frac{4\left(\frac{\sqrt{3}}{2}\cos 20° - \frac{1}{2}\sin 20°\right)}{\sin 20° \cos 20°}$</p><p><strong>Step 4:</strong> Recognize sine difference formula:</p><p>$= \frac{4(\sin 60° \cos 20° - \cos 60° \sin 20°)}{\sin 20° \cos 20°} = \frac{4\sin 40°}{\sin 20° \cos 20°}$</p><p><strong>Step 5:</strong> Use double angle formula $\sin 40° = 2\sin 20° \cos 20°$:</p><p>$= \frac{4 \cdot 2\sin 20° \cos 20°}{2\sin 20° \cos 20°} = 4$</p><p>∴ Answer is (d) 4.</p>