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受欢迎的三角函数 >

证明 (cos(u)sec(u))/(tan(u))=cot(u)

解答

证明

\frac{cos ( u ) sec ( u )}{tan ( u )} = cot (u)

解答

真

求解步骤

\frac{cos ( u ) sec ( u )}{tan ( u )} = cot (u)

调整左侧

\frac{cos ( u ) sec ( u )}{tan ( u )}

用 sin, cos 表示

\frac{cos ( u ) sec ( u )}{tan ( u )}

使用基本三角恒等式:

sec (x) = \frac{1}{cos ( x )}

= \frac{cos ( u ) \frac{1}{c o s ( u )}}{tan ( u )}

使用基本三角恒等式:

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

= \frac{cos ( u ) \frac{1}{c o s ( u )}}{\frac{s i n ( u )}{c o s ( u )}}

化简

\frac{cos ( u ) \frac{1}{c o s ( u )}}{\frac{s i n ( u )}{c o s ( u )}} : \frac{cos ( u )}{sin ( u )}

\frac{cos ( u ) \frac{1}{c o s ( u )}}{\frac{s i n ( u )}{c o s ( u )}}

使用分式法则:

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

= \frac{cos ( u ) \frac{1}{c o s ( u )} cos ( u )}{sin ( u )}

cos (u) \frac{1}{cos ( u )} cos (u) = \frac{1}{cos ( u )} cos^{2} (u)

cos (u) \frac{1}{cos ( u )} cos (u)

使用指数法则:

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

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

= \frac{1}{cos ( u )} cos^{1 + 1} (u)

数字相加:

1 + 1 = 2

= \frac{1}{cos ( u )} cos^{2} (u)

= \frac{\frac{1}{c o s ( u )} cos ^{2} ( u )}{sin ( u )}

乘

\frac{1}{cos ( u )} cos^{2} (u) : cos (u)

\frac{1}{cos ( u )} cos^{2} (u)

分式相乘:

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

= \frac{1 \cdot cos ^{2} ( u )}{cos ( u )}

乘以:

1 \cdot cos^{2} (u) = cos^{2} (u)

= \frac{cos ^{2} ( u )}{cos ( u )}

约分:

cos (u)

= cos (u)

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

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

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

使用基本三角恒等式:

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

= cot (u)

我们已展示，在两侧可以有相同的形式

\Rightarrow 真

流行的例子

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