The numbers 3 2 sin 2 α - 1 , 14 and 3 4 - 2 sin 2 α form first three terms of an A . P . , then its fifth term is

Step-by-step solution

Since, 3 2 sin 2 α - 1 , 14 and 3 4 - 2 sin 2 α are in AP . Therefore, 2 × 14 = 3 2 sin 2 α - 1 + 3 4 - 2 sin 2 α ⇒   28 = a 3 + 3 4 a , where a = 3 2 sin 2 α ⇒   a 2 - 84 a + 243 = 0 ⇒   a - 81 a - 3 = 0 ⇒   a = 81 ,   a = 3 ⇒   3 2 sin 2 α = 3 4 or 3 2 sin 2 α = 3 ⇒   2 sin 2 α = 1 ∵   2 sin 2 α ≠ 4 ⇒   sin 2 α = 1 2 ⇒ 2 α = 30 °    &#8