You are here:

Advanced Math/Trigonometric Identities

Advertisement


Question
5.4.4
Subject: PreCalculus - Topic: Sum & Difference Formulas/Identities

Hello, I have been working on this problem for over half an hour, but just cannot figure it out. I am asked to simply this expression using a sum or difference identity:
sin(x + y) * sec x * sec y

I have tried each of the Sum Identities and Difference Formulas that were taught (as well as in combinations), but cannot stop from being lost at solving this problem. If you could please show the answer, but more importantly, how you got that answer, it would be much appreciated. Thank you for your time, -John

Answer
Questioner:John
Country:Wisconsin, United States
Category:Advanced Math
Private:No
Subject:PreCalculus

Subject: PreCalculus - Topic: Sum & Difference Formulas/Identities

Hello, I have been working on this problem for over half an hour, but just cannot figure it out. I am asked to simply this expression using a sum or difference identity:
sin(x + y) * sec x * sec y

I have tried each of the Sum Identities and Difference Formulas that were taught (as well as in combinations), but cannot stop from being lost at solving this problem. If you could please show the answer, but more importantly, how you got that answer, it would be much appreciated. Thank you for your time, -John
.....................................

Try changing all to sines and cosines.  

[Shorthand to reduce typing: sin x = sx,  etc.]

sin(x + y) sec x sec y =

(sx cy + cx sy)sec x sec y =   <<<<<< standard sum formula

(sx cy + cx sy)(1/ cx) (1/ cy) =   <<<<<<< reciprocal identity

sx cy + cx sy
-------------- =
 cx  cy

sx cy    cx sy
------ + -------- =
cx cy    cx cy

sx     sy
---- + ---- =
cx     cy

tan x + tan y    <<<<<<<<<<< quotient identity

I suppose that should finish it.  

Advanced Math

All Answers


Answers by Expert:


Ask Experts

Volunteer


Paul Klarreich

Expertise

I can answer questions in basic to advanced algebra (theory of equations, complex numbers), precalculus (functions, graphs, exponential, logarithmic, and trigonometric functions and identities), basic probability, and finite mathematics, including mathematical induction. I can also try (but not guarantee) to answer questions on Abstract Algebra -- groups, rings, etc. and Analysis -- sequences, limits, continuity. I won't understand specialized engineering or business jargon.

Experience

I taught at a two-year college for 25 years, including all subjects from algebra to third-semester calculus.

Education/Credentials
-----------

©2016 About.com. All rights reserved.