Let cos α + β = 4 5 and let sin α - β = 5 13 , where 0 ≤ α , β ≤ π 4 , then tan 2 α =

Step-by-step solution

0 ≤ α , β ≤ π 4 ;   α + β ≤ π 2 cos ( α + β ) = 4 / 5 ⇒ tan ( α + β ) = 3 / 4 sin ( α - β ) = 5 / 13 ⇒ α - β ∈ θ 1 and tan ( α - β ) = 5 / 12 tan 2 α = tan ( α + β + α - β ) = tan ( α + β ) + tan ( α - β ) 1 - tan ( α + β ) tan ( α - β ) = 3 / 4 + 5 / 12 1 - 3 / 4 × 5 12 = 56 33