If 2 − cos2θ = 3 sinθ cosθ, where sinθ ≠ cosθ, the value of tanθ is.
If 2 − cos2θ = 3 sinθ cosθ, where sinθ ≠ cosθ, the value of tanθ is. Correct Answer 1/2
Calculation:
⇒ 2 − cos2θ = 3 sinθ cosθ
Dividing the expression by cos2θ,
⇒ 2 sec2θ – 1 = 3 tan θ
⇒ 2 (1 + tan2θ) – 1 = 3 tanθ
⇒ 2 tan2θ – 3 tanθ + 1 = 0
⇒ (2 tanθ – 1) (tanθ – 1) = 0
As given, sinθ ≠ cosθ
So, tanθ ≠ 1
⇒ 2tanθ = 1
⇒ tanθ = 1/2
∴ The value of tanθ is 1/2
Mistake Points
We can not put θ = 45° because sin θ ≠ cos θ.
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Feb 20, 2025