证明 (cos^2(x))/(sin^2(x))=cot^2(x)

解答

证明

\frac{cos ^{2} ( x )}{sin ^{2} ( x )} = cot^{2} (x)

真

求解步骤

\frac{cos ^{2} ( x )}{sin ^{2} ( x )} = cot^{2} (x)

调整右侧

cot^{2} (x)

用 sin, cos 表示

cot^{2} (x)

使用基本三角恒等式:

cot (x) = \frac{cos ( x )}{sin ( x )}

= (\frac{cos ( x )}{sin ( x )})^{2}

化简

(\frac{cos ( x )}{sin ( x )})^{2} : \frac{cos ^{2} ( x )}{sin ^{2} ( x )}

(\frac{cos ( x )}{sin ( x )})^{2}

使用指数法则:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{cos ^{2} ( x )}{sin ^{2} ( x )}

= \frac{cos ^{2} ( x )}{sin ^{2} ( x )}

= \frac{cos ^{2} ( x )}{sin ^{2} ( x )}

我们已展示，在两侧可以有相同的形式

\Rightarrow 真

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