证明 cos(4x)-cos(3x)cos(x)=sin(2x)-4cos(2x)sin(2x)

解答

证明

cos (4 x) - cos (3 x) cos (x) = sin (2 x) - 4 cos (2 x) sin (2 x)

假

求解步骤

cos (4 x) - cos (3 x) cos (x) = sin (2 x) - 4 cos (2 x) sin (2 x)

两侧不相等

对于

cos (4 x) - cos (3 x) cos (x) = sin (2 x) - 4 cos (2 x) sin (2 x)

代入

x = 1

cos (4 \cdot 1) - cos (3 \cdot 1) cos (1) = - 0.11874 \dots

cos (4 \cdot 1) - cos (3 \cdot 1) cos (1)

整理为小数形式

= - 0.11874 \dots

sin (2 \cdot 1) - 4 cos (2 \cdot 1) sin (2 \cdot 1) = 2.42290 \dots

sin (2 \cdot 1) - 4 cos (2 \cdot 1) sin (2 \cdot 1)

整理为小数形式

= 2.42290 \dots

两侧不相等

\Rightarrow 假

p ro v e cos (4 x) = 1 - 8 sin^{2} (x) cos (x)

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

p ro v e 6 cos^{2} (A) - 5 = 1 - 6 sin^{2} (A)

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

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