题目

已知cosα=,cos(α-β)=,且0＜β＜α＜.(1)求tan2α的值;(2)求β的值. 答案：解:(1)由cosα=,0＜α＜,得sinα==. tanα=4. ∴tan2α==. (2)由0＜β＜α＜,得0＜α-β＜.∵cos(α-β)=,∴sin(α-β)=. 又β=α-(α-β),∴cosβ=cos［α-(α-β)］=cosαcos(α-β)+sinαsin(α-β)=×+×=.∴β=.I have made many friends up till now, some of are intelligent and hardworking.