Question

plz it step by step..........

Answer 1

Answer :

Given,

x secθ + y tanθ = 2 cosθ ...(i)

x tanθ + y secθ = cotθ ...(ii)

Now, multiplying (i) by tanθ and (ii) by secθ, we get

x secθ tanθ + y tan²θ = 2 cosθ tanθ

x secθ tanθ + y sec²θ = cotθ secθ

On subtraction, we get

y (tan²θ - sec²θ) = 2 cosθ tanθ - cotθ secθ

⇒ y (- 1) = 2 cosθ (sinθ/cosθ) - (cosθ/sinθ) (1/cosθ)

⇒ - y = 2 sinθ - 1/sinθ

⇒ - y = (2 sin²θ - 1)/sinθ

⇒ y = (1 - 2 sin²θ)/sinθ

⇒ y = cos2θ/sinθ [∵ 1 - 2 sin²θ = cos2θ]

∴ y = cos2θ/sinθ ...(A)

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