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受欢迎的三角函数 >

证明 ((cos(x)sec(x)))/(tan(x))=cot(x)

解答

证明

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

解答

真

求解步骤

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

调整左侧

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

用 sin, cos 表示

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

使用基本三角恒等式:

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

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

使用基本三角恒等式:

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

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

化简

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

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

使用分式法则:

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

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

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

cos (x) \frac{1}{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)

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

数字相加:

1 + 1 = 2

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

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

乘

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

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

分式相乘:

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

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

乘以:

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

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

约分:

cos (x)

= cos (x)

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

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

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

使用基本三角恒等式:

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

= cot (x)

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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