证明 cos(2x)=-2sin(x^2)+1

解答

证明

cos (2 x) = - 2 sin (x^{2}) + 1

假

求解步骤

cos (2 x) = - 2 sin (x^{2}) + 1

两侧不相等

对于

cos (2 x) = - 2 sin (x^{2}) + 1

代入

x = 1

cos (2 \cdot 1) = - 0.41614 \dots

cos (2 \cdot 1)

整理为小数形式

= - 0.41614 \dots

- 2 sin (1^{2}) + 1 = - 0.68294 \dots

- 2 sin (1^{2}) + 1

整理为小数形式

= - 0.68294 \dots

两侧不相等

\Rightarrow 假

p ro v e tan (x) (cos (x) + cot (x)) = sin (x) + 1

p ro v e 1 + tan^{2} (6 0^{\circ}) = sec^{2} (6 0^{\circ})

p ro v e sin (x) = sin (x + 2 π)

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

p ro v e cos (3 x) = cos (x) (1 - 4 sin^{2} (x))