5.2 NOTES
Completed
Verifying Trig Identities
Pre Calc 5.2
Verifying Trig Identities
1. tanxcosx = sin x
what you see on the right of the equal is the answer you need to get to.
3. secxcotx = csc x
2. tanxcotx = 1
option 2
option 1
4. 1 ­ sin θ 2
________ cos θ
= cos θ
5. 1 + tan x =
tan 2x
2
_________ csc 2x
2 x 6. 1 + tan
__________ = sec2x
sin 2x+ cos2x
7. sec
2 θ(1 ­ sin
2 ) = 1
θ
option 1 (distribute)
=
=
=
=
=
=
option 2 (change into sine or
cosine right away)
=
=
option 3
8. cotxsinx = cosxsinx
cscx
option 1 (1 fraction)
=
option 2(separate)
9. tanxcscx = 1
secx
option 1 (separate)
option 2 (1 fraction)
option 3 (separate)
=
= tanxcscx
=
=
=
= =
=
secx
=
option 4
=
=
=
=
10. sinx cosx
cscx + = 1
secx
option 1
11. 1 +
1 = 1
2
2
sec x csc x option 1 (separate)
1 1 = 1
sec2x csc2x =
=
+
+
1
option 2 (1 fraction)
1 + 1 = =
=
1 1
1
2u + tan2u + cos 2u
12. sin
_________________
= sec u
sec u
option 1 (separate)
2u + cos 2u) + tan2u (sin
=
sec u
2u 1 + tan
= sec u
=
=
sec2u
sec u
sec u
option 2 (1 fraction)
=
sin2u + tan2u + cos 2u sec u
13. (sec2x + csc2x) ­ (tan 2x + cot2x) = 2
= sec x + csc x ­ tan x ­ cot x
= (sec x ­ tan x) + (csc x ­ cot x)
= 1 + 1
2 = 2
2
2
2
2
2
2
2
15. sinxtanx ­ secx = ­cosx
=
=
= =
­ cos x
= 16. (cscθ ­ secθ) sinθcosθ= cosθ ­ sinθ
option 1 (change into sine/cosine and distribute)
= ( ­ ) sinθcosθ =
=
=
17. 1 1 +
1­ cosx
2
1+ cosx = 2csc x
=
These are not Pythagorean identities.
=
you need to cross multiply
2
=
=
=
=
2
2
18. cosx sinx ­ cosx = secx
1­ sinx
This is not a Pythagorean identities.
you need to cross multiply
19. 1 + tanx = tanx
1 + cotx
Not a pythagorean identity!
option 2
option 1
=
optional
line
=
=
=
=
Not a pythagorean
identity!
5.2 Assignment:
Book Problems WPF for all
p 387: 2­22 Even,
25­29 All,
35­38 All