Checkout JEE MAINS 2022 Question Paper Analysis : Checkout JEE MAINS 2022 Question Paper Analysis :

sec^2theta = 4xy/(x + y)^2 is true if and only if

sec2θ = 4xy/(x + y)2 is true if and only if

1) x + y ≠ 0

2) x = y, x ≠ 0

3) x = y

4) x ≠ 0, y ≠ 0

Answer: (2) x = y, x ≠ 0

Solution:

Given,

sec2θ = 4xy/(x + y)2

We know that, sec2θ ≥ 1

Therefore, 4xy/(x + y)2 ≥ 1

4xy ≥ (x + y)2

⇒ (x + y)2 – 4xy ≤ 0

⇒ (x – y)2 ≤ 0

⇒ x – y = 0

⇒ x = y

Now,

x + y = 2x

Also, x + y ≠ 0 (denominator should not equal to 0)

2x ≠ 0

x ≠ 0

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