Trigonometry

Let cos(a + b) = 4/5 and let sin(a - b) = 5/13 where 0 ≤ a,b ≤ π/4. Then tan 2a is

  1. 20/17
  2. 25/16
  3. 56/33
  4. 19/12

Answer

cos(a + b) = 4/5

tan(a + b) = 3/4

sin(a - b) = 5/13

tan(a - b) = 5/12

tan 2a = tan[(a-b) + (a+b)]

= tan(a+b) + tan(a-b)/[1 - tan(a+b)tan(a-b)]

The correct option is C.