The number of values of x in the interval π 4 , 7 π 4 for which 14 cosec 2 x - 2 sin 2 x = 21 - 4 cos 2 x holds, is ______.

Step-by-step solution

Given x ∈ π 4 , 7 π 4 14 cosec 2 x - 2 sin 2 x = 21 - 4 cos 2 x = 21 - 4 1 - sin 2 x = 17 + 4 sin 2 x 14 sin 2 x - 6 sin 2 x = 17 Let sin 2 x = p 14 p - 6 p = 17 ⇒ 14 - 6 p 2 = 17 p 6 p 2 + 17 p - 14 = 0 p = - 7 2 , 2 3 ⇒ sin 2 x = 2 3 ⇒ sin x = ± 2 3 ∴ There are 4 solutions