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  1. If   5 sin2θ + 4cos2θ =
    9
    and 0 < θ <
    π
    then tanθ is equal to
    22
    1. 1
    2. 0
    3. –1
    4. 1
      4
Correct Option: A

5 sin2θ + 4cos2θ =
9
2

⇒  10 sin2θ + 8 cos2θ = 9
On dividing by cos2θ
10 sin2θ
+
8 cos2θ
=
9
= 9 sec2θ
cos2θcos2θcos2θ

⇒  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



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