<ol class="abc-list"><li><div class="list-item-paragraph">Prove that&nbsp;\(\sqrt{3}\sin{2\theta}+\cos{2\theta}-1=2\sin{\theta}(\sqrt{3}\cos{\theta}-\sin{\theta})\).<span class="inline-marks">[3]</span></div></li><li><div class="list-item-paragraph">Hence solve \(\sqrt{3}\sin{2\theta}+\cos{2\theta}+3\cos{\theta}-\sqrt{3}\sin{\theta}=1\), where&nbsp;\(0\leq\theta\leq360^{\circ}\).<span class="inline-marks">[5]</span></div></li></ol>

Prove that \(\sqrt{3}\sin{2\theta}+\cos{2\theta}-1=2\sin{\theta}(\sqrt{3}\cos{\theta}-\sin{\theta})\).

Hence solve \(\sqrt{3}\sin{2\theta}+\cos{2\theta}+3\cos{\theta}-\sqrt{3}\sin{\theta}=1\), where \(0\leq\theta\leq360^{\circ}\).

Trigonometric Equations and Identities

International Baccalaureate Standard Level Mathematics