Let α, β, and γ be some angles in the first quadrant satisfying tan(α+β)=15/8 and cosecγ=17/8, then which of the following hold(s) good?
α+β+γ=π
cot α cot β cot γ=cot α+cot β+cot γ
tan α+tan β+tan γ=tan α tan β tan γ
tan α tan β+tan β tan γ+tan γ tan α=1
tan(α+β)=158
and cosec γ=178
⇒ tan γ=815
∴ α+β+γ=π2
Hence, (2) is true.
Also tan(α+β)=tan α+tan β1−tan α tan β
or cot γ=tan α+tan β1−tan α tan β
or tan α tan β+tan β tan γ+tan γ tan α=1