Question

Eliminate θ from x = cot θ + tan θ; y = sec θ - cos θ

Answer 1

Please see the attachment

Answer 2

Answer:

(∛(y/x))² + (∛(1/x²y))² = 1

Step-by-step explanation:

x = cot θ + tan θ

=> x = Cosθ/Sinθ + Sinθ/Cosθ

=> x = (cos²θ + Sin²θ)/CosθSinθ

=> x = 1/CosθSinθ

y = Secθ - Cosθ

=> y = 1/Cosθ - Cosθ

=> y = ( 1 - Cos²θ)/Cosθ

=> y = Sin²θ/Cosθ

=> y = Sin³θ/CosSinθ

y/x  = Sin³θ

=> Sinθ = ∛(y/x)

x²y = 1/Cos³θ

=> Cos³θ = 1/x²y

=> Cosθ  = ∛(1/x²y)

Sin²θ  + Cos²θ = 1

=> (∛(y/x))² + (∛(1/x²y))² = 1