Question

Julia wants to simplity the term sec? a-1 in a trigonometric identity that she is proving. Which of the following identities should she use to help her? Select all that apply.
(1 point)
sin?@+cos?0=1
sec? @- tan° &= 1
الا
1
sec 8=
cos a
口
cot.8 =
1
tan €
1= csc? 0-cot? e

Answer 1

Select:
- sin^2 θ + cos^2 θ = 1
- sec^2 θ − tan^2 θ = 1 (equivalently sec^2 θ = 1 + tan^2 θ)
- sec θ = 1/cos θ

Reason: Using sec^2 = 1 + tan^2 gives sec^2 a − 1 = tan^2 a directly. Alternatively, sec a = 1/cos a and sin^2+cos^2=1 let you write (1/cos^2 a) − 1 = (1−cos^2 a)/cos^2 a = sin^2 a / cos^2 a = tan^2 a.