Question

tan(a+b)=2 sinc等于多少.当a=1c=根号5时.b为多少

Answer 1

tan(a+b)=2

tanC=-2

sinC/cosC=-2

sin^2C=4cos^2C

sin^2C = 4/5

sinC = 2√5/5

cosC = -√5/5

由余弦定理：

c^2=a^2+b^2-2abcosC

5 = 1+b^2+2√5/5b

整理

5b^2+2√5b-20=0

b=(√105-√5)/5