**Correct option (a) 2x = y**

**Explanation:**

2x = tan20° + tan50°

2y = tan20° + tan70°

2x = sin 20° .cos50° + cos 20° .sin 50°/cos 20° .cos 70°

2y = sin 20° .cos 70° cos 20° .sin 70°/cos 20° .cos 70°

2x = sin 70°/cos50° .cos 20°

2y = sin 90°/sin 20° .cos 20°

2x = cos 20°/cos50° .cos 20°

2y = sin 90°/sin20° .cos 20°

2x = cos 20°/cos50° .cos 20°

⇒ 2x = 1/cos50° 1/ sin 40° ...(1)

2y =2/ sin 40° .....................(2)

From (1) and (2)

2x = y