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Simplifying Trig. Identities

Simplifying Trig. Identities. Chapter5: Analytical Trigonometry. “Simplify identities to sin and cos functions.”. sin x. cos x. Simplifying trig Identity. Example1: simplify tan x cos x. tan x cos x. tan x cos x = sin x. sec x. sec x. sin x. sinx. 1. 1. 1. = tan x. =. =.

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Simplifying Trig. Identities

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  1. Simplifying Trig. Identities • Chapter5: Analytical Trigonometry “Simplify identities to sin and cos functions.”

  2. sin x cos x Simplifying trig Identity Example1: simplify tanxcosx tanx cosx tanxcosx = sin x

  3. sec x sec x sin x sinx 1 1 1 = tan x = = x cos x cos x cos x csc x csc x sin x 1 Simplifying trig Identity Example2: simplify

  4. cos2x - sin2x cos2x - sin2x cos2x - sin2x 1 = sec x cos x cos x Simplifying trig Identity Example2: simplify

  5. Practice

  6. Example Simplify: Factor out cot x = cot x (csc2 x - 1) Use pythagorean identity = cot x (cot2 x) Simplify = cot3 x

  7. = 1 = sin2 x + cos2x = sin x (sin x) + cos x = sin2 x + (cos x) cos x cos x cos x cos x cos x cos x Example Simplify: Use quotient identity Simplify fraction with LCD Simplify numerator Use pythagorean identity Use reciprocal identity = sec x

  8. Your Turn! Combine fraction Simplify the numerator Use pythagorean identity Use Reciprocal Identity

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