If 5 sin2θ + 4cos2θ = 9 and 0

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5 sin²θ + 4cos²θ =	9
	2

⇒ 10 sin²θ + 8 cos²θ = 9
On dividing by cos²θ

10 sin²θ	+	8 cos²θ	=	9	= 9 sec²θ
cos²θ		cos²θ		cos²θ

⇒ 10 tan²θ + 8 = 9 (1 + tan²θ)
⇒ 10 tan²θ + 8 = 9 + 9 tan²θ
⇒ 10 tan²θ – 9 tan²θ = 9 – 8
⇒ tan²θ = 1 ⇒ tan θ = ± 1

∵ 0 < θ <	π	, ∴ tanθ = 1
	2

If 5 sin²θ + 4cos²θ =	9	and 0 < θ <	π	then tanθ is equal to
	2		2