设θ∈(0,派)若sin(θ+7派/4)+cos(θ-3派/4)=根号5/2..则tan2θ等于多少
问题描述:
设θ∈(0,派)若sin(θ+7派/4)+cos(θ-3派/4)=根号5/2..则tan2θ等于多少
答
sin(θ+7π/4)+cos(θ-3π/4)=根号5/2∴ sin(θ-π/4+2π)+cos(θ+π/4-π)=根号5/2∴ sin(θ-π/4)-cos(θ+π/4)=根号5/2∴ sin(θ-π/4)-cos(θ-π/4+π/2)=根号5/2∴ 2 sin(θ-π/4)=根号...