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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

Questioner:John
Country:Wisconsin, United States
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.

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