If (1+tan⁡θ)(1+tan⁡ϕ)=2, then θ+ϕ=

If (1+tanθ)(1+tanϕ)=2, then θ+ϕ=

  1. A

    30

  2. B

    45

  3. C

    60

  4. D

    75

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    Solution:

    We have

    (1+tanθ)(1+tanϕ)=21+tanθ+tanϕ+tanθtanϕ=2tanθ+tanϕ=1tanθtanϕtanθ+tanϕ1tanθtanϕ=1tan(θ+ϕ)=1θ+ϕ=π4,nZ

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