已知π/2

题目

已知π/2

答案

sina=3/5
cosa=-4/5
cos(b-a)=cosb(-4/5)+(3/5)sinb=√(1-sin^2b)(-4/5)+(3/5)sinb=5/13
令sinb=x
则-4√(1-x^2)+3x=25/13
3x-25/13=4√(1-x^2)
9x^2+625/169-150x/13=16(1-x^2)
1521x^2+625-1950x=2704-2704x^2
4225x^2-1950x-2079=0
解得sinb=[1959+√(3802500+35135100)]/8450=(1959+6240)/8450=8199/8450