The document discusses trigonometric identities including fundamental identities relating sine, cosine, tangent, cotangent, secant and cosecant. It provides three examples of verifying trigonometric identities: relating secant and sine to tangent; relating tangent and cotangent to their reciprocals plus 1; and relating secant, cosine and sine to tangent.

1. Day 63
1. Trigonometric Identities

2. 1. Trigonometric Identities - Fundamental
Identities 1
csc x =
sin x
1
sec x =
cos x
1
cot x =
tan x
sin x
tan x =
cos x
cos x
cot x =
sin x
2 2
sin x + cos x = 1
2 2
1+ tan x = sec x
2 2
1+ cot x = csc x

3. 2. Examples
Verify the identity:
secθ sin θ = tan θ

4. 2. Examples
Verify the identity:
1+ tan x
= tan x
1+ cot x

5. 2. Examples
Verify the identity:
sec α − cos α = sin α tan α