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

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

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

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

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

csc x – 1 =

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