证明 (3csc(x)-3sin(x))/(tan(x)-cot(x))=3cos^3(x)

解答

证明

\frac{3 csc ( x ) - 3 sin ( x )}{tan ( x ) - cot ( x )} = 3 cos^{3} (x)

假

求解步骤

\frac{3 csc ( x ) - 3 sin ( x )}{tan ( x ) - cot ( x )} = 3 cos^{3} (x)

两侧不相等

对于

\frac{3 csc ( x ) - 3 sin ( x )}{tan ( x ) - cot ( x )} = 3 cos^{3} (x)

代入

x = 1

\frac{3 csc ( 1 ) - 3 sin ( 1 )}{tan ( 1 ) - cot ( 1 )} = 1.13706 \dots

\frac{3 csc ( 1 ) - 3 sin ( 1 )}{tan ( 1 ) - cot ( 1 )}

整理为小数形式

= 1.13706 \dots

3 cos^{3} (1) = 0.47318 \dots

3 cos^{3} (1)

整理为小数形式

= 0.47318 \dots

两侧不相等

\Rightarrow 假

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