If c o s α + β = 3 5 , sin ⁡ ( α - β ) = 5 13 and 0 < α , β < π 4 , then tan ⁡ 2 α is equal to:

Step-by-step solution

c o s α + β = 3 5 ⇒ t a n α + β = 4 3 s i n ( α - β ) = 5 13 ⇒ t a n ( α - β ) = 5 12 Now, t a n 2 α = t a n α + β + α - β = t a n ( α + β ) + t a n ( α - β ) 1 - t a n ( α + β ) t a n ( α - β ) = 4 3 + 5 12 1 - 4 3 × 5 12 = 63 16