If 2 s i n α 1 + c o s 2 α = 1 7 and 1 - c o s 2 β 2 = 1 10 , α ,   β ∈ 0 , π 2 , then t a n α + 2 β , is equal to

Step-by-step solution

Given, 2 sin α 1 + cos 2 α = 1 7 and 1 - cos 2 β 2 = 1 10 ,   α ,   β ∈ 0 , π 2 Now using cos 2 θ = 2 cos 2 θ - 1 = 1 - 2 sin 2 θ , we can write 2 sin ⁡ α 2 cos ⁡ α = 1 7 and 2 sin ⁡ β 2 = 1 10 tan ⁡ α = 1 7 and sin ⁡ β = 1 10 or tan ⁡ β = 1 3 t a n 2 β = 2 tan ⁡ β 1 - tan 2 ⁡ β = 2 . 1 3 1 - 1 9 = 3 4 tan ⁡ α + 2 β = t a n α + t a n 2 β