If α and β lies between 0 and (π/2) and if cos (α+β)=(12/13) and sin (α-β)=(3/5), then value of sin 2 α is

Question

If α and β lies between 0 and (π/2) and if cos (α+β)=(12/13) and sin (α-β)=(3/5), then value of sin 2 α is (A) (55/56) (B) (13/58) (C) 0 (D) (56/65)

Tardigrade Admin · Accepted Answer

sin (2 α)= sin (α+β+α-β) = sin (α+β) cos (α-β)+ cos (α+β) sin (α-β) =(5/13) ⋅ (4/5)+(12/13) ⋅ (3/5)=(56/65)

Q. If $α$ and $β$ lies between 0 and $\frac{π}{2}$ and if $cos (α + β) = \frac{12}{13}$ and $sin (α - β) = \frac{3}{5}$ , then value of $sin 2 α$ is