Question

已知Cos(x-派/4)=根号2/10,x属于(派/2,3派/4)求sinx的值.

Answer 1

cos（x－π／4）=cosxcosπ/4+sinxsinπ/4=(√2/2)(cosx+sinx)=√2/10

cosx+sinx=1/5

(cosx+sinx)^2=(cosx)^2+2cosxsinx+(sinx)^2

=1+2sinxcosx

=1/25

sinxcosx=-12/25

∵x∈（π／2,3π／4）

∴sinx>0

则cosx0

sinx-cosx=7/5

sinx=(1/5+7/5)÷2=4/5