证明 (sin(a))/(tan(a))=cos(a)

解答

证明

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

真

求解步骤

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

调整左侧

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

用 sin, cos 表示

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

使用基本三角恒等式:

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

= \frac{sin ( a )}{\frac{s i n ( a )}{c o s ( a )}}

化简

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

\frac{sin ( a )}{\frac{s i n ( a )}{c o s ( a )}}

使用分式法则:

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

= \frac{sin ( a ) cos ( 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 sin^{2} (3 x) + cos^{2} (3 x) = 1

p ro v e cos (\frac{π}{7}) = sin (\frac{π}{2} - \frac{π}{7})

p ro v e arctan (x) = \frac{arcsin ( x )}{arccos ( x )}

p ro v e \frac{csc ( θ ) + 1}{1 + sin ( θ )} = csc (θ)

p ro v e sec (A) csc (A) = csc (A) tan (A)