证明 sin(4x)=4sin(x)cos(x)

解答

证明

sin (4 x) = 4 sin (x) cos (x)

假

求解步骤

sin (4 x) = 4 sin (x) cos (x)

两侧不相等

对于

sin (4 x) = 4 sin (x) cos (x)

代入

x = 1

sin (4 \cdot 1) = - 0.75680 \dots

sin (4 \cdot 1)

整理为小数形式

= - 0.75680 \dots

4 sin (1) cos (1) = 1.81859 \dots

4 sin (1) cos (1)

整理为小数形式

= 1.81859 \dots

两侧不相等

\Rightarrow 假

p ro v e (1 + cot^{2} (θ)) tan^{2} (θ) = sec^{2} (θ)

p ro v e cot (θ) = sec (θ) csc (θ) - tan (θ)

p ro v e sin^{2} (β) csc^{2} (β) - sin^{2} (β) = cos^{2} (β)

p ro v e cot^{2} (a) - cos^{2} (a) = cot^{2} (a) cos^{2} (a)

p ro v e cos^{2} (θ) (sec^{2} (θ) - 1) = sin^{2} (θ)