证明 9sec(y)cos(y)=9

解答

证明

9 sec (y) cos (y) = 9

真

求解步骤

9 sec (y) cos (y) = 9

调整左侧

9 sec (y) cos (y)

用 sin, cos 表示

9 cos (y) sec (y)

使用基本三角恒等式:

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

= 9 cos (y) \frac{1}{cos ( y )}

9 cos (y) \frac{1}{cos ( y )} = 9

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

分式相乘:

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

= \frac{1 \cdot 9 cos ( y )}{cos ( y )}

约分:

cos (y)

= 1 \cdot 9

数字相乘:

1 \cdot 9 = 9

= 9

= 9

= 9

我们已展示，在两侧可以有相同的形式

\Rightarrow 真

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

p ro v e tan^{2} (x) + 2 = sec^{2} (x) + 1

p ro v e tan^{2} (t) sin^{2} (t) = tan^{2} (t) - sin^{2} (t)

p ro v e 8 sin^{2} (θ) + 9 cos^{2} (θ) = 8 + cos^{2} (θ)

p ro v e sec^{2} (x) + tan^{2} (x) = 1 + 2 tan^{2} (x)