Prove that : tanθsecθ−1 - tanθsecθ+1 = 2 cotθ
LHS = tanθsecθ−1 - tanθsecθ+1
= tanθ(secθ+1)−tanθ(secθ−1)sec2θ−1
= tanθsecθ+tanθ−tanθsecθ−tanθsec2θ−1
= 2tanθtan2θ
= 2tanθ=2cotθ (RHS)