Решите : 13 sin(x+y) , если sin x = 4/5 cos y = 12/13 и x,y - острые углы. Created by Dasdas123123123. algebra-ru

13 и x,y - острые углы...

August 2022 2 7 Report

Решите : 13 sin(x+y) , если sin x = 4/5 cos y = 12/13 и x,y - острые углы

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Используя основное тригонометрическое тождество, получаем:
cosx = √1 - sin²x = √1 - 16/25 = 3/5
siny = √1 - cos²y = √1 - 144/169 = √25/169 = 5/13
13sin(x + y) = 13·(sinxcosy + cosxsiny) = 13·(4/5·12/13 + 3/5·5/13) = 48/65 + 3/13 = 13·(48/65 + 15/65) =13·63/65 = 12,6

1 votes Thanks 2

sedinalana Сosx=√(1-sin²x)=√(1-16/25)=√(9/25)=3/5
siny=√(1-cos²y)=√(1-144/169)=√(25/169)=5/13
13sin(x+y)=13(sinxcosy+cosxsiny)=13(4/5*12/13+3/5*5/13)=
=13(48/65+15/65)=13*63/65=63/5=12,6

1 votes Thanks 1

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