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Algebra 2: Lesson 12-8 Simplifying Trig Expressions
Learning Goals:
1. How can we use Trig identities to simplify a trig expression?
2. How can we use the Pythagorean Identity to simplify a trig expression?
Remember:
Pythagorean Identity
Reciprocal Identities
Directions: Simplify each expression.
1) 1 cos2 
2) (sin )(csc )
3) (tan )(cot )
4) (tan )(csc )
Quotient Identities
5) (sin2  )(cos )(tan )(csc )
7) tan cos 
9)
tan cos
sin
6)
csc
sec
8)
tan 
sin
10) (sin  cos )2
11) Prove that the following is a trigonometric identity, beginning with the side of the equation
that seems to be more complicated. Make sure that the complete identity statement is
included at the end of the proof.
tan( x) 
sec( x)
for real numbers
csc( x)
, for all integers .
12) Prove that the following is a trigonometric identity, beginning with the side of the equation
that seems to be more complicated. Make sure that the complete identity statement is
included at the end of the proof.
cot(x)  tan(x)  sec( x) csc( x) for all real numbers
for integer .