证明 cos(10x)-cos(6x)=-2sin(8x)sin(2x)

解答

证明

cos (10 x) - cos (6 x) = - 2 sin (8 x) sin (2 x)

真

求解步骤

cos (10 x) - cos (6 x) = - 2 sin (8 x) sin (2 x)

调整左侧

cos (10 x) - cos (6 x)

使用三角恒等式改写

cos (10 x) - cos (6 x)

使用和差化积恒等式:

cos (s) - cos (t) = - 2 sin (\frac{s + t}{2}) sin (\frac{s - t}{2})

= - 2 sin (\frac{10 x + 6 x}{2}) sin (\frac{10 x - 6 x}{2})

化简

- 2 sin (\frac{10 x + 6 x}{2}) sin (\frac{10 x - 6 x}{2}) : - 2 sin (8 x) sin (2 x)

- 2 sin (\frac{10 x + 6 x}{2}) sin (\frac{10 x - 6 x}{2})

\frac{10 x + 6 x}{2} = 8 x

\frac{10 x + 6 x}{2}

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

p ro v e sec (y) - cos (y) = tan (y) sin (y)

p ro v e sin (5 x) - sin (3 x) = 2 cos (4 x) sin (x)

p ro v e sin (4 0^{\circ}) = 2 sin (2 0^{\circ}) cos (2 0^{\circ})

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