证明 (sin^2(t))/(tan(t))=sin(t)cos(t)

解答

证明

\frac{sin ^{2} ( t )}{tan ( t )} = sin (t) cos (t)

真

求解步骤

\frac{sin ^{2} ( t )}{tan ( t )} = sin (t) cos (t)

调整左侧

\frac{sin ^{2} ( t )}{tan ( t )}

用 sin, cos 表示

\frac{sin ^{2} ( t )}{tan ( t )}

使用基本三角恒等式:

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

= \frac{sin ^{2} ( t )}{\frac{s i n ( t )}{c o s ( t )}}

化简

\frac{sin ^{2} ( t )}{\frac{s i n ( t )}{c o s ( t )}} : sin (t) cos (t)

\frac{sin ^{2} ( t )}{\frac{s i n ( t )}{c o s ( t )}}

使用分式法则:

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

= \frac{sin ^{2} ( t ) cos ( t )}{sin ( t )}

约分:

sin (t)

= sin (t) cos (t)

= sin (t) cos (t)

= cos (t) sin (t)

= sin (t) cos (t)

我们已展示，在两侧可以有相同的形式

\Rightarrow 真

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p ro v e - sec^{2} (x) = - \frac{1}{cos ^{2} ( x )}

p ro v e sin (2 x) = 3 sin (x)

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