Use ubtraction Formula to write the expression as a trigonometric function of one number.(cos)(13pi)/15cos(-pi/5)-(sin)(13pi)/15sin(-pi/5)

SchachtN 2021-09-13 Answered
Use an Addition or Subtraction Formula to write the expression as a trigonometric function of one number, and then find its exact value.
(cos)13π15cos(π5)(sin)13π15sin(π5)
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Expert Answer

Bertha Stark
Answered 2021-09-14 Author has 96 answers
Our expression is
(cos)13π15cos(π5)(sin)13π15sin(π5)
This kind of expression appears on the addition of angles formula for cosine
cos(x+y)=cosxcosysinxsiny
with x=13π15,y=π5
So we have
(cos)13π15cos(π5)(sin)13π15sin(π5)=cos(13π15+(π5))
=cos(13π153π15)
=(cos)10π15
=(cos)2π3
=cos(π3)[cos(πx)=cosx]
=12
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