Costheta/1-sintheta + sintheta /1-costheta = costheta + sin theta
Answers
Given data is wrong
Step-by-step explanation:
Cosθ/(1 - Sinθ) + Sinθ/(1 - Cosθ) = Cosθ + Sinθ
LHS
= Cosθ/(1 - Sinθ) + Sinθ/(1 - Cosθ)
= Cosθ(1 + Sinθ)/(1 - Sinθ)(1 + Sinθ) + Sinθ(1 + Cosθ)/(1 - Cosθ)(1+ Cosθ)
= (Cosθ + CosθSinθ)/(1 - Sin²θ) + (Sinθ + SinθCosθ)/(1 - Cos²θ)
= (Cosθ + CosθSinθ)/(Cos²θ) + (Sinθ + SinθCosθ)/(Sin²θ)
= (1 + Sinθ)/(Cosθ) + (1 + Cosθ)/(Sinθ)
= (Sinθ + Sin²θ + Cosθ + Cos²θ)/CosθSinθ
= (1 + Sinθ + Cosθ)/(SinθCosθ)
Cosθ/(1 - Sinθ) + Sinθ/(1 - Cosθ) = Cosθ + Sinθ is wrong
for example θ = 45°
LHS = (1/√2)/(1 - 1/√2) + (1/√2)/(1 - 1/√2)
= 1/(√2 - 1) + 1/(√2 - 1)
= 2/√2 - 1
= 2(√2 + 1)
RHS
= 1/√2 + 1/√2
= √2
LHS ≠ RHS
Given data is wrong
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