证明 sin(a)cos(a)=cos^2(a)tan(a)

解答

证明

sin (a) cos (a) = cos^{2} (a) tan (a)

真

求解步骤

sin (a) cos (a) = cos^{2} (a) tan (a)

调整右侧

cos^{2} (a) tan (a)

用 sin, cos 表示

cos^{2} (a) tan (a)

使用基本三角恒等式:

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

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

化简

cos^{2} (a) \frac{sin ( a )}{cos ( a )} : sin (a) cos (a)

cos^{2} (a) \frac{sin ( a )}{cos ( a )}

分式相乘:

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

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

约分:

cos (a)

= sin (a) cos (a)

= sin (a) cos (a)

= cos (a) sin (a)

= sin (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 (- \frac{π}{4}) = - sin (\frac{π}{4})

p ro v e sin (z + w) = sin (z) cos (w) + cos (z) sin (w)

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

p ro v e cos (0) tan (0) = sin (0)

p ro v e cos (\frac{π}{6}) = \frac{4}{3} cos^{3} (\frac{π}{6})