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Verifying Trigonometric Identities

5.2. Verifying Trigonometric Identities. Place sec 2 x under both terms. 1 - cos 2 x =. sin 2 x = sin 2 x. 1. 1. +. =. 2 sec 2 x. 1 - sin x. 1 + sin x. (tan 2 x + 1)(cos 2 x - 1) = -tan 2 x. (sec 2 x)(-sin 2 x) =. tan x + cot x = sec x csc x.

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Verifying Trigonometric Identities

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  1. 5.2 Verifying Trigonometric Identities Place sec2 x under both terms. 1 - cos2 x = sin2 x = sin2 x

  2. 1 1 + = 2 sec2 x 1 - sin x 1 + sin x

  3. (tan2 x + 1)(cos2 x - 1) = -tan2 x (sec2 x)(-sin2 x) =

  4. tan x + cot x = sec x csc x Get common denominators. sec x cscx = sec x csc x

  5. sec y + tan y = We need a (1 – sin y) in the denominator so let’s put one there. cos y

  6. csc x – 1 =

  7. tan4 x = tan2 x sec2 x - tan2 x Look at the right side. How can we break up tan4 x? (tan2 x)(tan2 x) = tan2 x(sec2 x - 1) = tan2 x sec2 x - tan2 x = tan2 x sec2 x - tan2 x

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