If θ is a positive acute angle and 3 (sec²θ

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If θ is a positive acute angle and 3 (sec²θ + tan²θ) = 5, then the value of cos 2θ is

(sec²θ + tan²θ) = 5

⇒ sec²θ + tan²θ =	5
	3

⇒ sec²θ + sec²θ - 1 =	5
	3

⇒ 2 sec²θ =		5	+ 1 =	8
		3		3

⇒ sec²θ =		4	⇒ secθ =	2
		3		√3

⇒ cosθ =	√3	= cos 30°
	2

⇒ θ = 30°

∴ cos 2θ = cos 60° =	1
	2

	1
	√2