证明 7sec(y)cos(y)=7

解答

证明

7 sec (y) cos (y) = 7

真

求解步骤

7 sec (y) cos (y) = 7

调整左侧

7 sec (y) cos (y)

用 sin, cos 表示

7 cos (y) sec (y)

使用基本三角恒等式:

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

= 7 cos (y) \frac{1}{cos ( y )}

7 cos (y) \frac{1}{cos ( y )} = 7

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

分式相乘:

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

= \frac{1 \cdot 7 cos ( y )}{cos ( y )}

约分:

cos (y)

= 1 \cdot 7

数字相乘:

1 \cdot 7 = 7

= 7

= 7

= 7

我们已展示，在两侧可以有相同的形式

\Rightarrow 真

p ro v e sec (\frac{π}{2} - u) = csc (u)

p ro v e \frac{cot ^{3} ( t )}{csc ( t )} = cos (t) (csc^{2} (- 1))

p ro v e \frac{sec ^{2} ( x ) cot ( x )}{csc ^{2} ( x )} = tan (x)

p ro v e \frac{sec ^{2} ( y )}{tan ( y )} = tan (y) + cot (y)

p ro v e cos (6 x) = 1 - 2 sin^{2} (3 x)