The number of solutions of the equation t a n 2 x - s e c 10 x + 1 = 0 for x ∈ 0,20 is equal to

Step-by-step solution

s e c 2 x - s e c 10 x = 0 s e c 2 x 1 - s e c 8 x = 0 1 - s e c 8 x = 0 as s e c 2 x ≥ 1 ⇒ s e c 8 x = 1 ⇒ c o s 8 x = 1 ⇒ c o s x = ± 1 ⇒ x = n π ,   ∀ n ∈ Ι ⇒ x = π , 2 π , 3 π , 4 π , 5 π , 6 π ∈ 0,20 So, the required number of roots = 6