本题目来源于试卷: Trigonometric Functions，类别为 IB数学
[问答题]
1. Solve the equatiorl9hb tapo(mul 0b- /yw.ktsm +-i61r, y*o*b4bce.c (k gy6yyc4v jwn $\sin \left(x+90^{\circ}\right)=2 \cos \left(x-60^{\circ}\right)$, $0^{\circ} \lt x\lt360^{\circ} $.
2. Show that $\sin 15^{\circ}+\cos 15^{\circ}=\frac{\sqrt{6}}{2}$ .
3. Let $z=1-\cos 4 \theta-\mathrm{i} \sin 4 \theta$ , for $ z \in \mathbb{C}, 0<\theta<\frac{\pi}{2}$ .
1. Find the modulus and argument of z . Express each answer in its simplest form.
2. Hence find the fourth roots of z in modulus-argument form.
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