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29 vote

If 5sin2θ + 4cos2θ = 9/2 and 0 < θ < π/2, then cot θ is equal to?

Asked on by | Votes 29 | Views: 137 | Tags: trigonometry     | quantitative aptitude     | Add Bounty

If 5sin2θ + 4cos2θ = 9/2 and 0 < θ < π/2, then cot θ is equal to?
1). 1
2). 0
3). ­-1
4). ¼


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1 answers

23 vote
Answered by on | Votes 23 |

5sin2θ + 4cos2θ = 9/2

⇒ sin2θ + 4sin2θ + 4cos2 θ = 9/2

⇒ sin2θ + 4(sin2θ + cos2 θ) = 9/2

⇒ sin2θ + 4 = 9/2

⇒ sin2θ = 9/2 – 4

⇒ sin2θ = ½

⇒ sin θ = 1/√2

⇒ θ = 45°

∴ cot 45° = 1
Accepted Answer

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