If sinθ=35,cosϕ=1213 where θ,ϕ∈(0,π/2), then the value of tan(θ+ϕ) is
A
833
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B
733
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C
3356
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D
5633
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Solution
The correct option is D5633 We have θ,ϕ∈(0,π/2) So sinθ=35⇒cosθ=√1−sin2θ=45⇒tanθ=34 Similarily, cosϕ=1213,⇒sinϕ=513,tanϕ=512 tan(θ+ϕ)=tanθ+tanϕ1−tanθtanϕ=34+5121−34×512=5633