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HMMT 二月 2009 · 冲刺赛 · 第 2 题

HMMT February 2009 — Guts Round — Problem 2

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. [ 5 ] Given that sin A + sin B = 1 and cos A + cos B = 3 / 2, what is the value of cos( A − B )?
解析
  1. [ 5 ] Given that sin A + sin B = 1 and cos A + cos B = 3 / 2, what is the value of cos( A − B )? Answer: 5 / 8 Solution: Squaring both equations and add them together, one obtains 1+9 / 4 = 2+2(cos( A ) cos( B )+ sin( A ) sin( B )) = 2 + 2 cos( A − B ). Thus cos A − B = 5 / 8.