Helen's Blog

Section 10-1

Formulas:

cos(alpha +/- beta) cos alpha cos beta -/+ sin alpha sin beta
sin(alpha +/- beta) sin alpha cos beta +/- cos alpha sin beta

Examples:

Ex1:Find the exact value of sin15

sin(45-30)=sin45cos30-cos45sin30
=(√2/2)(√3/2)-(√2/2)(1/2)
=√6-√2/4


Section 10-2 ( same concept but tan instead)

Formula:

tan(alpha + beta)= tan (alpha) + tan (beta) / 1-tan(alpha) tan(beta)

tan(alpha - beta)= tan(alpha)- tan (beta) / 1+tan(alpha)tan(beta)

Ex2:

Simplify: tan27+tan18/1-tan27tan18

=tan(27+18)
=tan45
=1