证明 csc(2x)= 1/(sin^2(x)-1)

解答

证明

csc (2 x) = \frac{1}{sin ^{2} ( x ) - 1}

假

求解步骤

csc (2 x) = \frac{1}{sin ^{2} ( x ) - 1}

两侧不相等

对于

csc (2 x) = \frac{1}{sin ^{2} ( x ) - 1}

代入

x = 1

csc (2 \cdot 1) = 1.09975 \dots

csc (2 \cdot 1)

整理为小数形式

= 1.09975 \dots

\frac{1}{sin ^{2} ( 1 ) - 1} = - 3.42551 \dots

\frac{1}{sin ^{2} ( 1 ) - 1}

整理为小数形式

= - 3.42551 \dots

两侧不相等

\Rightarrow 假

p ro v e (1 + tan^{2} (α)) (1 - sin^{2} (α)) = 1

p ro v e csc (θ) - cot (θ) = \frac{1 - cos ( θ )}{sin ( θ )}

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

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

p ro v e cot (u) = \frac{1}{tan ( u )}