If $1 + sin^2 θ – 3sinθ cosθ = 0$, then the value of $cotθ$ is:
Answer & explanation
Correct answer: option 2
We are given :-
1 + sin²θ - 3sinθ.cosθ = 0
1 + sin²θ = 3sinθ.cosθ
{ put sin²θ+ cos²θ = 1 }
sin²θ+ cos²θ + sin²θ = 3sinθ.cosθ
cos²θ + 2sin²θ = 3sinθ.cosθ
cos²θ + sin²θ - 2sinθ.cosθ + sin²θ = sinθ.cosθ
( cosθ -sinθ)² = sinθ( cosθ - sinθ)
cosθ -sinθ = sinθ
2sinθ = cosθ
ATQ,
cotθ = 2