Question

已知sin(3π+θ)=1/4 求cos(π+θ)/cosθ[cos(π+θ)-1] +cos(θ

已知sin(3π+θ)=1/4
求cos(π+θ)/cosθ[cos(π+θ)-1] +cos(θ-2π)/cos(θ+2π)cos(π+θ)+cos(-θ)的值

Answer 1

sin(3π+θ)=1/4

sin(π+θ)=1/4
-sinθ=1/4
sinθ=-1/4
cosθ=±√(1-sin^2θ)=±√15/4
cos(π+θ)/cosθ[cos(π+θ)-1] +cos(θ-2π)/cos(θ+2π)cos(π+θ)+cos(-θ)

=-cosθ/cosθ[-cosθ-1]+cosθ/cosθ(-cosθ)+cosθ
=cosθ+1-cosθ+cosθ
=cosθ
=±√15/4

Answer 2

sin(3π+θ)=sin(π+θ)=-sinθ=1/4
sinθ=-1/4
cos(π+θ)/cosθ[cos(π+θ)-1] +cos(θ-2π)/cos(θ+2π)cos(π+θ)+cos(-θ)

=-cosθ/cosθ[-cosθ-1] +cosθ/cosθ(-cosθ)+cosθ

=1/(cosθ+1)-1/cosθ+cosθ