If secθ+tanθ=y,secθ+tanθ=y, simplify y21y2+1 in terms of θ.


Answer:

sinθ

Step by Step Explanation:
  1. y21y2+1=(secθ+tanθ)21(secθ+tanθ)2+1=sec2θ+tan2θ+2tanθsecθ1sec2θ+tan2θ+2tanθsecθ+1=(sec2θ1)+tan2θ+2tanθsecθsec2θ+(1+tan2θ)+2tanθsecθ=2tan2θ+2tanθsecθ2sec2θ+2tanθsecθ=2tanθ(tanθ+secθ)2secθ(tanθ+secθ)=sinθ

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