Proof of the Difference Formula for Sine and of the Addition Formula for Cosine

sin or cos

show tip

α or π/2-α

1.257

β

0.524

remove cos(β) sin(β)

remove cos(α) sin(α)

remove 2 cos(α) sin(β) or 2 sin(α) sin(β)

This Demonstration shows a proof of the difference formula for sine,

sin(α-β)=sin(α)cos(β)-cos(α)sin(β)

and a proof of the addition formula for cosine,

cos(α+β)=cos(α)cos(β)-sin(α)sin(β)

using the formula

cos(α+β)=sin(π/2-(α+β))

.

External Links

Addition Formula for Sine

Difference Formula for Cosine

Trigonometric Functions (Wolfram MathWorld)

Permanent Citation

Izidor Hafner

"Proof of the Difference Formula for Sine and of the Addition Formula for Cosine"
http://demonstrations.wolfram.com/ProofOfTheDifferenceFormulaForSineAndOfTheAdditionFormulaFor/
Wolfram Demonstrations Project
Published: December 6, 2010