Download x2 + 1 Expression x2 + 1 = 5 x2 + x = x(x + 1)

November 21, 2014
Section 5.2 Verifying Trigonometric Identities
Objective: Know how to verify trigonometric identities.
x2 + 1
Expression
x2 + 1 = 5
Equation (true for only some values in the domain)
"Solve"
x2 + x = x(x + 1)
Identity (true for all real #s in the domain)
"Verify"
Note: There are no set techniques that you apply every time when
verifying identities. Following are guidelines, which can be found on p.348
of the text...just guidelines!
Work with only one side of the equation at a time. Usually it is better to
start with the more complicated side first.
Look for opportunities to factor an expression, add fractions, square a
binomial, or create a single-term denominator.
Look for opportunities to use the fundamental identities. Note which
functions are in the final expression you want. Sine and cosine pair well,
as do secant and tangent, and cosecant and cotangent.
As a last resort, convert all terms to sine and cosine.
Always try something! Even paths that lead to dead ends give you insight.
November 21, 2014
Ex1: Verify the identity.
a)
sin2x - 1 = -cot x
sin2x
b)
1
1
= 2cot x
sec x - 1
sec x + 1
2
2
c c) (1 + cot x)(1 - sin x) = cot x
2
2
Ex2: Verify these identities.
1
a) sec u + tan u =
sec u - tan u
b) cot t cos t = csc t - sin t
c)
1 - sin x
cot2x
=
1 + csc x
sin x
2
Mo
re!
November 21, 2014
Try this one!
sin x (csc x - 1)(csc x + 1) = 1 - sin x
2
2