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jaiprakash111
@jaiprakash111
August 2021
1
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plz it step by step..........
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MarkAsBrainliest
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)
#MarkAsBrainliest
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Answers & Comments
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)
#MarkAsBrainliest