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If 1 + sin2 - 3sin cos = 0 then the...

This question belongs to Arithmetic Ability Trigonometry
Trigonometry
?

If 1 + sin2θ - 3sinθcosθ = 0, then the value of cotθ is:

Answer & Solution
Correct Answer: Option A
1 + sin2θ - 3sinθ.cosθ = 0
⇒ 1 - 2sinθ.cosθ = sinθ.cosθ - sin2θ
⇒ sin2θ + cos2θ - 2sinθ.cosθ = sinθ(cosθ - sinθ)
⇒ (cosθ - sinθ)2 = sinθ(cosθ - sinθ)
⇒ cosθ - sinθ = sinθ
⇒ cosθ = 2sinθ
⇒ cotθ = 2
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