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cosβ=sinα
sinα*sinβ=3/4
sinα*cosα=3/4
cosα+cosβ=cosα+sinα
(sinα+cosα)²=1+2sinαcosα
(sinα+cosα)²=1+2*3/4=1+3/2=5/2
cosβ+cosα=√5/2=√5/√2= √(5*2)/2
cosα+cosβ=√10/2