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受欢迎的三角函数 >

证明 (csc(z))/(sec(z))=cot(z)

解答

证明

\frac{csc ( z )}{sec ( z )} = cot (z)

解答

真

求解步骤

\frac{csc ( z )}{sec ( z )} = cot (z)

调整左侧

\frac{csc ( z )}{sec ( z )}

用 sin, cos 表示

\frac{csc ( z )}{sec ( z )}

使用基本三角恒等式:

csc (x) = \frac{1}{sin ( x )}

= \frac{\frac{1}{s i n ( z )}}{sec ( z )}

使用基本三角恒等式:

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

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

化简

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

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

分式相除:

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

= \frac{1 \cdot cos ( z )}{sin ( z ) \cdot 1}

整理后得

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

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

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

使用基本三角恒等式:

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

= cot (z)

我们已展示，在两侧可以有相同的形式

\Rightarrow 真

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