This document discusses strategies for verifying identities in trigonometry. It notes that verifying identities involves showing that the left-hand side and right-hand side are equal. Common strategies include working with the more complicated side of the identity, writing all terms in terms of basic trig functions like sine, cosine, and tangent, and replacing combinations with simpler expressions or common denominators to show the two sides are equal. The document provides some examples of identities to verify and assigns problems numbers 6 through 12.
1. Verifying/ Proving Identities
show that two items are identical
sin csc = 1
To show LHS = RHS
Usually work with one side only -
the more complicated side
sec = 1 cos = 1
csc = 1 sin = 1
cot = cos tan = sin
2. + 1 = sec
Some strategies to Verify:
Work with more complicated side
As needed write everything in terms of
sin , cos , tan , usually
Replace more complicated combos with
simpler expressions
replace with
replace with
replace with
Try to write all terms over same denominator
cos
3. Show that 1 + cot
tan + cot = sec csc
csc - sin = cot cos
