if 1 + sin squared theta is equal to 3 sin theta cos theta then prove that tan theta is equal to 1 or 10 theta is equal to 1 by 2
Answers
this is best way to prove the answer
Proved Tanθ = 1 or 1/2 if 1 + Sin²θ = 3SinθCosθ
Step-by-step explanation:
1 + Sin²θ = 3SinθCosθ
=> 1 + Sin²θ = 2SinθCosθ + SinθCosθ
using 1 = Sin²θ + Cos²θ
=> Sin²θ + Cos²θ + Sin²θ = 2SinθCosθ + SinθCosθ
=> Sin²θ + Cos²θ - 2SinθCos + Sin²θ - SinθCosθ = 0
=> (Sinθ - Cosθ)² + Sinθ(Sinθ - Cosθ) = 0
=> (Sinθ - Cosθ)(Sinθ - Cosθ + Sinθ)= 0
=> (Sinθ - Cosθ)(2Sinθ - Cosθ)= 0
Sinθ - Cosθ = 0
=> Sinθ = Cosθ
=> Tanθ = 1
2Sinθ - Cosθ = 0
=> 2Sinθ = Cosθ
=> Tanθ = 1/2
Hence proved Tanθ = 1 or 1/2 if 1 + Sin²θ = 3SinθCosθ
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