证明 (sin(2θ))/(sin(θ))=2

解答

证明

\frac{sin ( 2 θ )}{sin ( θ )} = 2

假

求解步骤

\frac{sin ( 2 θ )}{sin ( θ )} = 2

两侧不相等

对于

\frac{sin ( 2 θ )}{sin ( θ )} = 2

代入

θ = 1

\frac{sin ( 2 \cdot 1 )}{sin ( 1 )} = 1.08060 \dots

\frac{sin ( 2 \cdot 1 )}{sin ( 1 )}

整理为小数形式

= 1.08060 \dots

两侧不相等

\Rightarrow 假

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

p ro v e - 2 sin (2 x + π) = - 2 sin (2 x - π)

p ro v e 2 sin (a + b) sin (a - b) = cos (2 b) - cos (2 a)

p ro v e \frac{1}{sin ( x )} = 2

p ro v e 5 sec^{2} (x) = 5 sec^{2} (- x)