Identities Practice Sheet #2—Show work on a separate sheet of paper!!
Simplify each expression:
1. cscx – cosx·cotx
2. sinx + sinx·cot2x
4. cos2x·tan2x + cos2x
5. (secx – tanx)(1 + sinx)
Check answers for #1-5 (not in order)
3.
1
sin x
sin x
+
1  cos x
1  cos x
sinx
cosx
cscx
2cscx
cscx
2cscx
Verify that each equation is an identity: (yes, all of them are identities!!)
1  tan 2 x
sin x  cos x
6.
= tan x
7.
= sec x + csc x
sin x cos x
csc x sec x
8. sinx·tanx = secx – cosx
9. (sinx – 1)(tanx + secx) = –cosx
Identities Practice Sheet—Show work on a separate sheet of paper!!
Simplify each expression:
1. cscx – cosx·cotx
2. sinx + sinx·cot2x
4. cos2x·tan2x + cos2x
5. (secx – tanx)(1 + sinx)
Check answers for #1-5 (not in order)
3.
1
sin x
sin x
+
1  cos x
1  cos x
sinx
cosx
Verify that each equation is an identity: (yes, all of them are identities!!)
1  tan 2 x
sin x  cos x
6.
= tan x
7.
= sec x + csc x
sin x cos x
csc x sec x
8. sinx·tanx = secx – cosx
9. (sinx – 1)(tanx + secx) = –cosx
Hints:
1.
2.
3.
4.
5.
6.
7.
8.
9.
rewrite in terms of sin/cos, combine fractions, substitute, then cancel.
factor out sin x, then use substitution, rewrite, then cancel.
get common denominator, use FOIL method, make a substitution and cancel.
factor common term, make a substitution, rewrite, and cancel
rewrite in terms of sin/cos, combine fractions (subtract 1st, then multiply), substitute, cancel
substitute Pythagorean identity, cancel, rewrite in terms of sin/cos, invert and solve
split apart fraction, cancel, rewrite
rewrite secx, get common denominator, substitute, split apart numerator, simplify
use FOIL method, rewrite in terms of sin/cos, combine fractions, factor –1 from numerator, substitute, cancel
Hints:
1.
2.
3.
4.
5.
6.
7.
8.
9.
rewrite in terms of sin/cos, combine fractions, substitute, then cancel.
factor out sin x, then use substitution, rewrite, then cancel.
get common denominator, use FOIL method, make a substitution and cancel.
factor common term, make a substitution, rewrite, and cancel
rewrite in terms of sin/cos, combine fractions (subtract 1st, then multiply), substitute, cancel
substitute Pythagorean identity, cancel, rewrite in terms of sin/cos, invert and solve
split apart fraction, cancel, rewrite
rewrite secx, get common denominator, substitute, split apart numerator, simplify
use FOIL method, rewrite in terms of sin/cos, combine fractions, factor –1 from numerator, substitute, cancel