(a) 证明方程

可写成 $a\cos^2x+b\cos x+c=0$ 的形式，其中 $a$、$b$ 和 $c$ 是待求的整数。

(b) 由此，在 $0^\circ\le x\le360^\circ$ 内解方程 $4\sin x+\frac{5}{\tan x}+\frac{2}{\sin x}=0$。

Answer all questions. You should use a calculator where appropriate.

You must show all necessary working clearly; no marks will be given for unsupported answers from a calculator.

Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question.

请回答所有题目。适当时应使用计算器。必须清楚展示所有必要的计算过程；仅给出计算器答案而没有过程，不予评分。除非题目另有精度要求，非精确数值答案保留 3 位有效数字，以度为单位的角度保留 1 位小数。

先在原式的定义域中同乘 $\sin x$，再把正弦平方换成余弦平方。

Where the original expression is defined, $\sin x\ne0$ and $\tan x=\sin x/\cos x$. Multiplying by $\sin x$ gives

Using $\sin^2 x=1-\cos^2 x$ and multiplying by $-1$ gives $4\cos^2 x-5\cos x-6=0$. Thus $(a,b,c)=(4,-5,-6)$.

分解关于 $\cos x$ 的二次式，舍去超出余弦值域的根，再找区间内的两个角。

The equation factors as $(4\cos x+3)(\cos x-2)=0$. Since $\cos x=2$ is impossible, $\cos x=-3/4$. The solutions are $138.6^\circ$ and $221.4^\circ$, to one decimal place. Both belong to the domain of the original equation.