If x = secθ + cosecθ and y = sinθcosθ, then, what is the value of y(x2y – 2)?
If x = secθ + cosecθ and y = sinθcosθ, then, what is the value of y(x2y – 2)? Correct Answer 1
Given:
x = secθ + cosecθ
y = sinθcosθ
Formula Used:
sin2θ + cos2θ = 1
Calculation:
x = secθ + cosecθ
⇒ x = 1/cosθ + 1/sinθ
⇒ x = (sinθ + cosθ)/sinθcosθ
Squaring both sides –
⇒ x2 = (sin2θ + cos2θ + 2sinθcosθ)/(sinθcosθ)2
⇒ x2 = (1 + 2y)/y2
⇒ x2y2 = 1 + 2y
⇒ x2y2 – 2y = 1
⇒ y(x2y – 2) = 1
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Feb 20, 2025