证明 2cos(x)tan(x)cot(x)=2

解答

证明

2 cos (x) tan (x) cot (x) = 2

假

求解步骤

2 cos (x) tan (x) cot (x) = 2

两侧不相等

对于

2 cos (x) tan (x) cot (x) = 2

代入

x = 1

2 cos (1) tan (1) cot (1) = 1.08060 \dots

2 cos (1) tan (1) cot (1)

整理为小数形式

= 1.08060 \dots

两侧不相等

\Rightarrow 假

p ro v e sec (2 x) = \frac{csc ( x )}{csc ( x ) - 2 sin ( x )}

p ro v e \frac{1}{arctan ( x )} = arccot (x)

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

p ro v e cot (θ) \cdot sec (θ) = \frac{1}{cos ( θ )}

p ro v e sin (x) sin (y) = 2 sin (\frac{x + y}{2}) cos (\frac{x - y}{2})