证明 sec^3(x)= 1/(cos^3(x))

解答

证明

sec^{3} (x) = \frac{1}{cos ^{3} ( x )}

真

求解步骤

sec^{3} (x) = \frac{1}{cos ^{3} ( x )}

调整左侧

sec^{3} (x)

用 sin, cos 表示

sec^{3} (x)

使用基本三角恒等式:

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

= (\frac{1}{cos ( x )})^{3}

化简

(\frac{1}{cos ( x )})^{3} : \frac{1}{cos ^{3} ( x )}

(\frac{1}{cos ( x )})^{3}

使用指数法则:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{1 ^{3}}{cos ^{3} ( x )}

使用法则

1^{a} = 1

1^{3} = 1

= \frac{1}{cos ^{3} ( x )}

= \frac{1}{cos ^{3} ( x )}

= \frac{1}{cos ^{3} ( x )}

我们已展示，在两侧可以有相同的形式

\Rightarrow 真

p ro v e 4 cos^{2} (B) - 4 sin^{2} (B) = 4 - 8 sin^{2} (B)

p ro v e cos (4 A) = 8 cos^{4} (A) - 8 cos^{2} (A) + 1

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