证明 4sec(y)cos(y)=4

解答

证明

4 sec (y) cos (y) = 4

真

求解步骤

4 sec (y) cos (y) = 4

调整左侧

4 sec (y) cos (y)

用 sin, cos 表示

4 cos (y) sec (y)

使用基本三角恒等式:

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

= 4 cos (y) \frac{1}{cos ( y )}

4 cos (y) \frac{1}{cos ( y )} = 4

4 cos (y) \frac{1}{cos ( y )}

分式相乘:

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

= \frac{1 \cdot 4 cos ( y )}{cos ( y )}

约分:

cos (y)

= 1 \cdot 4

数字相乘:

1 \cdot 4 = 4

= 4

= 4

= 4

我们已展示，在两侧可以有相同的形式

\Rightarrow 真

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

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

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

p ro v e cot (a) sin (a) = cos (a)

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