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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

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.

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Answers by Expert:

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.

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

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