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受欢迎的三角函数 >

证明 cot(x)sin(x)sec(x)=1

解答

证明

cot (x) sin (x) sec (x) = 1

解答

真

求解步骤

cot (x) sin (x) sec (x) = 1

调整左侧

cot (x) sin (x) sec (x)

用 sin, cos 表示

cot (x) sec (x) sin (x)

使用基本三角恒等式:

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

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

使用基本三角恒等式:

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

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

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

\frac{cos ( x )}{sin ( x )} \cdot \frac{1}{cos ( x )} sin (x)

分式相乘:

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

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

约分:

cos (x)

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

约分:

sin (x)

= 1

= 1

= 1

我们已展示，在两侧可以有相同的形式

\Rightarrow 真

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