zs

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

受欢迎的三角函数 >

证明 (cot(x))/(cos(x))=csc(x)

解答

证明

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

解答

真

求解步骤

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

调整左侧

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

用 sin, cos 表示

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

使用基本三角恒等式:

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

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

化简

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

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

使用分式法则:

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

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

约分:

cos (x)

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

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

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

使用三角恒等式改写

使用基本三角恒等式:

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

\frac{1}{\frac{1}{c s c ( x )}}

化简

\frac{1}{\frac{1}{c s c ( x )}}

使用分式法则:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

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

使用法则

\frac{a}{1} = a

= csc (x)

csc (x)

csc (x)

我们已展示，在两侧可以有相同的形式

\Rightarrow 真

流行的例子

证明 (sin(x)cos(x))/(tan(x))=cos^2(x)

p ro v e \frac{sin ( x ) cos ( x )}{tan ( x )} = cos^{2} (x)

证明 2sin^2(2t)+cos(4t)=1

p ro v e 2 sin^{2} (2 t) + cos (4 t) = 1

证明 (cos(θ)+cos(3θ))/(2cos(2θ))=cos(θ)

p ro v e \frac{cos ( θ ) + cos ( 3 θ )}{2 cos ( 2 θ )} = cos (θ)

证明 sin(270+x)=-cos(x)

p ro v e sin (27 0^{\circ} + x) = - cos (x)

证明 (1+sin(α))(1-sin(α))=cos^2(α)

p ro v e (1 + sin (α)) (1 - sin (α)) = cos^{2} (α)