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If 2 − cos2θ = 3 sin θ cos θ, where sin θ ≠ cos θ, the value of tan θ is.

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If 2 − cos2θ = 3 sin θ cos θ, where sin θ ≠ cos θ, the value of tan θ is.


1). 1
2). 1/2
3). √3
4). 1/√3


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1 answers

2 vote
Answered by on | Votes 2 |

As,

⇒ 2 − cos2θ = 3 sinθcosθ

Dividing the expression by cos2θ,

⇒ 2 sec2θ - 1 = 3 tan θ

⇒ 2 (1 + tan2θ) - 1 = 3 tan θ

⇒ 2 tan2θ - 3 tan θ + 1 = 0

⇒ (2 tan θ − 1) (tan θ − 1) = 0

As given, sinθ ≠ cosθ. So, tanθ ≠ 1

⇒ 2tan θ = 1

∴ tanθ = ½

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