Verifying Trigonometric Identities

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Pre calculus Problem of the Day
Homework p. 578 1-21 odds
Simplify the following:
  2   2
a) sin   cos 
 6   6 
  2   2
b) sin   cos 
 4   4 
 4  2  4  2
c) sin   cos 
 3  
3 
Trigonometric Identities - a statement of equality that is
true for all values where the function is defined.
Reciprocal Identities:

1
sin 
csc 
1
cos 
sec 
1
tan  
cot 
1
csc  
sin 
1
sec  
cos
1
cot  
tan 
Quotient Identities:

sin
tan  
cos
cos
cot  
sin
Pythagorean Identities:
Even/Odd Identities:
sin 2   cos2   1
sin   sin
1 cot 2   csc 2 
cos   cos
tan  1  sec 
2
2



tan   tan
Verifying Trigonometric Identities
To verify a trigonometric identity we must show that one side of
the identity can be simplified so that it is identical to the other
side or each side can be simplified independently until they are
identical.
Never treat an identity like an equation. We are not solving
for the variable.
Techniques for verifying trigonometric identities.
1) Rename using the fundamental identities.
2) Rewrite a more complicated side in terms of sines and
cosines.
3) Factor.
4) Combine fractional expressions using an LCD.
5) Separate a single-term quotient into two terms.
6) Multiply the numerator and denominator on one side by a
binomial factor that appears on the other side of the
identity.
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