Question

帮忙算一道函数题 17cosA+13cosB=17,17sinA=13sinB,且角A和角B斗士锐角,求1/2角A+角B

Answer 1

17cosA+13cosB=17 (1)

17sinA-13sinB=0 (2)

(1)^2+(2)^2=>

289cosA*cosA+169cosB*cosB+2*13*17*cosA*cosB=289

289sinA*sinA+169sinB*sinB-2*13*17*sinA*sinB=0

169+442*cos(A+B)=0

=>cos(A+B)=-13/34

角A和角B都是锐角,所以

（A+B）/2=~56度.