If 2 sin2 x + cos2 45° = tan 45° and x is an acute angle, then the v

1.	If 2 sin2 x + cos2 45° = tan 45° and x is an acute angle, then the value of tan x is:(a) 1 (b) √3 (c) \(\frac1{\sqrt3}\)(d) 3
Answer» (c) \(\frac1{\sqrt3}\) 2 sin² \(x\) + cos² 45° = tan 45° ⇒ 2 sin²\(x\) + \(\bigg(\frac1{\sqrt2}\bigg)^2\) = 1 ⇒ 2 sin²\(x\) = \(1-\frac12=\frac12\) ⇒ sin²\(x\) = \(\frac14\) ⇒ sin \(x\) = \(\frac12\) = sin 30° ⇒ \(x\) = 30° ∴ tan \(x\) = tan 30° = \(\frac1{\sqrt3}\).

If 2 sin2 x + cos2 45° = tan 45° and x is an acute angle, then the value of tan x is:(a) 1 (b) √3 (c) \(\frac1{\sqrt3}\)(d) 3

Answer»

(c) \(\frac1{\sqrt3}\)

2 sin² \(x\) + cos² 45° = tan 45°

⇒ 2 sin²\(x\) + \(\bigg(\frac1{\sqrt2}\bigg)^2\) = 1

⇒ 2 sin²\(x\) = \(1-\frac12=\frac12\)

⇒ sin²\(x\) = \(\frac14\) ⇒ sin \(x\) = \(\frac12\) = sin 30° ⇒ \(x\) = 30°

∴ tan \(x\) = tan 30° = \(\frac1{\sqrt3}\).