given that sin(x+y)=sinxcosy+cosxsiny use complementary identity and show that cos(x+y)=cosxcosy-sinxsiny?
回答 (1)
2020-04-25 7:21 pm
Trigonometric identities used:
cos(A) = sin(90° - A)
sin(A) = cos(90° - A)
sin(A + B) = sin(A) cos(B) + cos(A) sin(B)
cos(-A) = cos(A)
sin(-A) = -sin(A)
cos(x + y)
= sin[90° - (x + y)]
= sin[(90° - x) + (-y)]
= sin(90° - x) cos(-y) + cos(90° - x) sin(-y)
= cos(x) cos(y) + sin(x) [-sin(y)]
= cos(x) cos(y) - sin(x) sin(y)
cos(A) = sin(90° - A)
sin(A) = cos(90° - A)
sin(A + B) = sin(A) cos(B) + cos(A) sin(B)
cos(-A) = cos(A)
sin(-A) = -sin(A)
cos(x + y)
= sin[90° - (x + y)]
= sin[(90° - x) + (-y)]
= sin(90° - x) cos(-y) + cos(90° - x) sin(-y)
= cos(x) cos(y) + sin(x) [-sin(y)]
= cos(x) cos(y) - sin(x) sin(y)
收錄日期: 2021-04-12 12:51:13
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20200425104851AAnNHjd