※ 引述《Honor1984 (奈何上天造化弄人？)》之銘言：
: ※ 引述《MITjuching (CP3亞洲代言人)》之銘言：
: : http://i.imgur.com/foBHc6S.jpg
: : 第三題的cos(a-b)
: : 目前只算到
: : 8/9=sina*cosa+cosb*sinb+(cosacosb+sinasinb)
: : 不知道 sina*cosa+cosb*sinb 怎麼算
: : 求各位大大幫個忙
: : -----
: : Sent from JPTT on my Samsung SM-T320.
: sin(a) + cos(b) = 2/3
: cos(a) + sin(b) = 4/3
: => (1/2)[sin(2a) + sin(2b)] + cos(a - b) = 8/9
: => sin(a + b)cos(a - b) + cos(a - b) = 8/9
: => cos(a - b)[1 + sin(a + b)] = 8/9
: 由上一篇求得之cos(a - b)可得sin(a + b) = 1/9
: 或是由你先前已求出的sin(a + b) = 1/9可求得cos(a - b) = 4/5
兩邊相加得
[cos(alpha)+sin(alpha)]+[cos(beta)+sin(beta)]=2
再平方相加
[sin(2alpha)+sin(2beta)]+2[sin(alpha+beta) + cos(alpha-beta)]=2
2sin(alpha+beta)cos(alpha-beta)+(2/9)+2cos(alpha-beta)=2
cos(alpha-beta)
=(9/20)*(16/9)=4/5...ans
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