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MATH 1163 Precalculus Mathematics Fall 2013

Can Solve Identities:
A Trigonometric Identity Project

You have been asked to use your skills with identities to solve a few trigonometric
crimes that have recently occurred in your area. You may work with a partner (one
only) if you would like to solve the following five cases. You should compile a report
detailing your work for each case. For each case, you should clearly identify and explain
all steps involved in your solutions. Your completed report should be presented in a
professional manner and submitted directly to Professor Adams no later than 2:00
PM on Friday, November 22. Late submissions will not be accepted. The Project
is worth a maximum value of 50 points. Good luck on your mission!

• Case # 1: The Con Artist
You think you have tracked down the con artist

csc (x) − cot (x) ,

but he has hidden his true identity. If you can verify that

sin (x)

1 + cos (x)

is in fact his cover up identity, then you will have finally caught the infamous con
artist.

• Case # 2: Witness Protection Program
The officials in the Witness Protection Program have lost one of their protected
members. You have been asked to determine if

1

1 − cot (x)

is using the identity
sin (x)

sin (x) − cos (x)
If you can prove the identity is true, you will be able to help them find their
witness.

• Case # 3: Identity Theft
We have a case of identity theft! 2 cos (x) has had her identity stolen. Various
charges have been made against

cot (x) [cos (x) tan (x) + sin (x)]

on her behalf. Determine if they are actually the same so that her identity may
be returned.

• Case # 4: The Stolen Diamond
Trig Jewelers is asking for your help. They think that one of their largest diamonds
has been stolen and replaced with a diamond that has a fake serial number. The
diamond’s serial number is:

csc4 (x) − cot4 (x) .

The diamond that is now in the case has the following serial number:

2 csc2 (x) − 1.

In order to prove that the diamond in the case is an imposter, you need to verify
that the two diamonds are actually the same.

• Case # 5: Bank Robbers
The local police department has apprehended a group of bank robbers. When they
ran their names through the criminal database, the database indicated that the
bank robbers are on the list of America’s Most Wanted and they are each using an
alias. To obtain the rewards for each bank robber, the police department needs to
match the criminal with the appropriate alias. They need your help to determine
which identity is the appropriate alias.

Robbers Aliases

1. cscx− sinx a. − cos
2 x

(sinx + 1)2

2.
sinx

sinx + cosx
b. secx

3. 2 sin 4x cos 4x c. cosx cotx

4. 1 + tanx tan
x

2
d. sin 8x

5.
sinx− 1
sinx + 1

e.
tanx

1 + tan x