What is the recommended method to simplify trigonometric expressions like sin ⁡ α − sin ⁡ β cos ⁡ α − cos ⁡ β ?I tried to manipulate them using double and sum but none of them seemed to help.

Question

What is the recommended method to simplify trigonometric expressions like             sin      ⁡      α      −      sin      ⁡      β              cos      ⁡      α      −      cos      ⁡      β      ?I tried to manipulate them using double and sum but none of them seemed to help.

Kaitlyn Levine · Accepted Answer

sin      ⁡      α      −      sin      ⁡      β              cos      ⁡      α      −      cos      ⁡      β        =            2      sin      ⁡                        α          −          β                2            cos      ⁡                        α          +          β                2                    2      sin      ⁡                        β          −          α                2            sin      ⁡                        α          +          β                2              =  −  cot  ⁡            α      +      β        2    .The second is similar.

What is the recommended method to simplify trigonometric expressions like (sin alpha- sin beta)/( cos alpha- cos beta)

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