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受欢迎的三角函数 >

证明 (tan(x))/(cot(x))=tan^2(x)

解答

证明

\frac{tan ( x )}{cot ( x )} = tan^{2} (x)

解答

真

求解步骤

\frac{tan ( x )}{cot ( x )} = tan^{2} (x)

调整左侧

\frac{tan ( x )}{cot ( x )}

用 sin, cos 表示

\frac{tan ( x )}{cot ( x )}

使用基本三角恒等式:

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

= \frac{\frac{s i n ( x )}{c o s ( x )}}{cot ( x )}

使用基本三角恒等式:

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

= \frac{\frac{s i n ( x )}{c o s ( x )}}{\frac{c o s ( x )}{s i n ( x )}}

化简

\frac{\frac{s i n ( x )}{c o s ( x )}}{\frac{c o s ( x )}{s i n ( x )}} : \frac{sin ^{2} ( x )}{cos ^{2} ( x )}

\frac{\frac{s i n ( x )}{c o s ( x )}}{\frac{c o s ( x )}{s i n ( x )}}

分式相除:

\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{a \cdot d}{b \cdot c}

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

sin (x) sin (x) = sin^{2} (x)

sin (x) sin (x)

使用指数法则:

a^{b} \cdot a^{c} = a^{b + c}

sin (x) sin (x) = sin^{1 + 1} (x)

= sin^{1 + 1} (x)

数字相加:

1 + 1 = 2

= sin^{2} (x)

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

cos (x) cos (x) = cos^{2} (x)

cos (x) cos (x)

使用指数法则:

a^{b} \cdot a^{c} = a^{b + c}

cos (x) cos (x) = cos^{1 + 1} (x)

= cos^{1 + 1} (x)

数字相加:

1 + 1 = 2

= cos^{2} (x)

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

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

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

使用三角恒等式改写

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

使用基本三角恒等式:

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

\frac{sin ( x ) tan ( x )}{cos ( x )}

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

使用基本三角恒等式:

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

tan (x) tan (x)

化简

tan (x) tan (x) : tan^{2} (x)

tan (x) tan (x)

使用指数法则:

a^{b} \cdot a^{c} = a^{b + c}

tan (x) tan (x) = tan^{1 + 1} (x)

= tan^{1 + 1} (x)

数字相加:

1 + 1 = 2

= tan^{2} (x)

tan^{2} (x)

tan^{2} (x)

我们已展示，在两侧可以有相同的形式

\Rightarrow 真

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