Question

已知cosa-2sina=根号5 求tana的值

Answer 1

cosα-2sinα=√5

(cosα-2sinα)^2=5

cos^2α-4cosαsinα+4sin^2α=5

(cos^2α-4cosαsinα+4sin^2α)/(cos^2α+sin^2α)=5

左边上下同除以cos^2α

得到

(4tan^2α-4tanα+1)/(tan^2α+1)=5

4tan^2α-4tanα+1=5(tan^2α+1)

(tanα+2)^2=0

tanα=-2.