利用积化和差公式sinαcosβ=1/2[sin(α+β)+sin(α-β)]
[sin(θ-α)cosθ]/cos²α
=1/2[sin(θ-α+θ)+sin(θ-α-θ)] /cos²α
=1/2[sin(2θ-α)+sin(-α)] /cos²α
所以sin(2θ-α)=1时,该式有最大值.
此时2θ-α=π/2,θ=π/4+α/2.