证明 2cos(2x)-1=1-2sin(2x)

解答

证明

2 cos (2 x) - 1 = 1 - 2 sin (2 x)

假

求解步骤

2 cos (2 x) - 1 = 1 - 2 sin (2 x)

两侧不相等

对于

2 cos (2 x) - 1 = 1 - 2 sin (2 x)

代入

x = 1

2 cos (2 \cdot 1) - 1 = - 1.83229 \dots

2 cos (2 \cdot 1) - 1

整理为小数形式

= - 1.83229 \dots

1 - 2 sin (2 \cdot 1) = - 0.81859 \dots

1 - 2 sin (2 \cdot 1)

整理为小数形式

= - 0.81859 \dots

两侧不相等

\Rightarrow 假

p ro v e sin (x) = tan (x) \cdot cos (x)

p ro v e tan^{2} (x) csc^{2} (x) - 1 = tan (x)

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

p ro v e cos (0 + \frac{π}{2}) = - sin (θ)

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