证明 cot(a)sin(a)=cos(a)

解答

证明

cot (a) sin (a) = cos (a)

真

求解步骤

cot (a) sin (a) = cos (a)

调整左侧

cot (a) sin (a)

用 sin, cos 表示

cot (a) sin (a)

使用基本三角恒等式:

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

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

化简

\frac{cos ( a )}{sin ( a )} sin (a) : cos (a)

\frac{cos ( a )}{sin ( a )} sin (a)

分式相乘:

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

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

约分:

sin (a)

= cos (a)

= cos (a)

= cos (a)

我们已展示，在两侧可以有相同的形式

\Rightarrow 真

p ro v e \frac{1 - cos ( x )}{sec ( x ) - 1} = cos (x)

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

p ro v e tan (- x) = tan (x)

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

p ro v e csc (x) \cdot cos^{2} (x) + sin (x) = csc (x)