Is cos(α+β)-cos(α-β)=-2sin(α)cos(β) ?

The answer to whether cos(α+β)-cos(α-β)=-2sin(α)cos(β) is False

prove cos(α+β)-cos(α-β)=-2sin(α)cos(β)

prove

cos (α + β) - cos (α - β) = - 2 sin (α) cos (β)

False

Solution steps

cos (α + β) - cos (α - β) = - 2 sin (α) cos (β)

Show that the two sides are not equal

For

cos (α + β) - cos (α - β) = - 2 sin (α) cos (β)

plug in

α = 1

For

cos (α + β) - cos (α - β) = - 2 sin (α) cos (β)

plug in

β = π

cos (1 + π) - cos (1 - π) = 0

cos (1 + π) - cos (1 - π)

Refine to a decimal form

= 0

- 2 sin (1) cos (π) = 1.68294 \dots

- 2 sin (1) cos (π)

Refine to a decimal form

= 1.68294 \dots

The two sides are not equal

\Rightarrow False

\frac{cot ( x )}{sin ( x )} = 1

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

\frac{1 - ( cos ( - x ) )}{sec ( - x ) - 1} = cos (x)

\frac{2}{2} csc (x) - 1 = 0

cos (2 (\frac{7 π}{4}) - \frac{π}{2}) = - 1

Is cos(α+β)-cos(α-β)=-2sin(α)cos(β) ?
The answer to whether cos(α+β)-cos(α-β)=-2sin(α)cos(β) is False