Products to Sums and Differences (Leaving Cert Mathematics): Flashcards

Trig identities that transform products into sums/differences

Products of sine/cosine into sums or differences

$\frac{1}{2}[\sin(A + B) + \sin(A - B)]$

$\frac{1}{2}[\sin(A + B) - \sin(A - B)]$

$\frac{1}{2}[\cos(A + B) + \cos(A - B)]$

$-\frac{1}{2}[\cos(A + B) - \cos(A - B)]$

Addition and subtraction identities for sine and cosine

Simplify expressions, solve equations, evaluate integrals

$\frac{1}{2}[\sin 5x + \sin x]$

$\frac{1}{2}[\cos 6x + \cos 2x]$

Simplify complex expressions and make equations manageable