证明 2cot^2(x)sin^2(x)=1+2cos(x)

解答

证明

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

假

求解步骤

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

两侧不相等

对于

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

代入

x = 1

2 cot^{2} (1) sin^{2} (1) = 0.58385 \dots

2 cot^{2} (1) sin^{2} (1)

整理为小数形式

= 0.58385 \dots

1 + 2 cos (1) = 2.08060 \dots

1 + 2 cos (1)

整理为小数形式

= 2.08060 \dots

两侧不相等

\Rightarrow 假

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

p ro v e 2 sin (z) cos (z) = sin (2 z)

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

p ro v e \frac{sin ^{2} ( θ )}{cos ( θ )} + cos (θ) = sec (θ)

p ro v e csc (u) - sin (u) = cot (u) cos (u)