1. Verifying Trigonometric
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 sec x cscx = 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