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Question

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 D 5633
We have θ,ϕ(0,π/2)
So sinθ=35cosθ=1sin2θ=45tanθ=34
Similarily,
cosϕ=1213,sinϕ=513,tanϕ=512
tan(θ+ϕ)=tanθ+tanϕ1tanθtanϕ=34+512134×512=5633

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