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PreCalculus Class Notes TEI2 Simplifying and Factoring Trigonometric Expressions Many of the algebraic skills that you have already learned can be used to simplify trigonometric functions. 1. Multiplying binomials (1 − x)(1 − x) 2. Adding two expressions y x y x + (1 − cosθ )(1 − cosθ ) tan t + cot t 3. Factoring an expression Difference of squares x2 − 1 sec2 θ − 1 x2 + x sin 2 x + sin x x2 + 2x + 1 tan 2 θ + 2 tan θ + 1 Common Factor Trinomials Simplify the trigonometric expression completely. 1 cos 2 θ − sin θ sin θ 1 − cos 2 θ 1 + cosθ Multiply out first If you convert to sin/cos first, you get csc 2 θ sec 2 θ . Is it equivalent? (cot θ + tan θ ) 2 csc 2 θ + sec 2 θ = csc 2 θ sec 2 θ sin 2 θ cscθ sin 2 t (1 + cot 2 t ) Factor the trigonometric expression and simplify, if possible. sin 2 t − cos 2 t cosθ sin 2 θ + cos3 θ sin 4 t − cos 4 t tan 2 x + 4 tan x − 12 csc x cot 2 x + 6 csc x cot x − 27 csc x 2 sin 2 x + 3sin x − 2