The solution of the equation 4 cos2 x + 6 sin2 x = 5 are (a) x = nπ

1.	The solution of the equation 4 cos2 x + 6 sin2 x = 5 are (a) x = nπ ± \(\frac{π}{4}\) (b) x = nπ ± \(\frac{π}{3}\)(c) x = nπ ± \(\frac{π}{2}\) (d) x = nπ ± \(\frac{2π}{3}\)
Answer» Answer : (a) \(x = nπ ± \frac{π}{4}\) 4 cos² x + 6 sin² x = 5 ⇒ 4 (cos² x + sin² x) + 2 sin² x = 5 ⇒ 2 sin² x = 5 – 4 = 1 ⇒ sin² x = \(\frac{1}{2}\) ⇒ sin x = ± \(\frac{1}{√2}\) ⇒ \(x = nπ ± \frac{π}{4}\)

The solution of the equation 4 cos2 x + 6 sin2 x = 5 are (a) x = nπ ± \(\frac{π}{4}\) (b) x = nπ ± \(\frac{π}{3}\)(c) x = nπ ± \(\frac{π}{2}\) (d) x = nπ ± \(\frac{2π}{3}\)

Answer»

Answer : (a) \(x = nπ ± \frac{π}{4}\)

4 cos² x + 6 sin² x = 5

⇒ 4 (cos² x + sin² x) + 2 sin² x = 5

⇒ 2 sin² x = 5 – 4 = 1 ⇒ sin² x = \(\frac{1}{2}\)

⇒ sin x = ± \(\frac{1}{√2}\)

⇒ \(x = nπ ± \frac{π}{4}\)