x ∈ R: cos 2x + 2 cos2 x = 2 is equal to(a) 2nπ + \(\frac{π}{3}\

1.	x ∈ R: cos 2x + 2 cos2 x = 2 is equal to(a) 2nπ + \(\frac{π}{3}\) , n ∈ Z(b) nπ ± \(\frac{π}{6}\), n ∈ Z(c) nπ + \(\frac{π}{3}\) , n ∈ Z(d) 2nπ - \(\frac{π}{3}\), n ∈ Z
Answer» Answer : (b) nπ ± \(\frac{π}{6}\), n ∈ Z cos 2x + 2 cos²x = 2 ⇒ 2 cos²x – 1 + 2 cos²x = 2 ⇒ 4 cos² x = 3 ⇒ cos x = ± \(\frac{\sqrt{3}}{2}\) ⇒ x = nπ ± \(\frac{π}{6}\), n∈Z

x ∈ R: cos 2x + 2 cos2 x = 2 is equal to(a) 2nπ + \(\frac{π}{3}\) , n ∈ Z(b) nπ ± \(\frac{π}{6}\), n ∈ Z(c) nπ + \(\frac{π}{3}\) , n ∈ Z(d) 2nπ - \(\frac{π}{3}\), n ∈ Z

Answer»

Answer : (b) nπ ± \(\frac{π}{6}\), n ∈ Z

cos 2x + 2 cos²x = 2

⇒ 2 cos²x – 1 + 2 cos²x = 2

⇒ 4 cos² x = 3

⇒ cos x = ± \(\frac{\sqrt{3}}{2}\)

⇒ x = nπ ± \(\frac{π}{6}\), n∈Z