sec^2 x = 4xy/(x + y)^2 is true if and only if A. x + y ≠ 0 B. x + y, x ≠ 0 C. x = y D. x ≠ 0, y ≠ 0

Question

sec² x = \(\cfrac{4\text xy}{(\text x+y)^2}\) is true if and only if 

A. x + y ≠ 0

B. x + y, x ≠ 0

C. x = y

D. x ≠ 0, y ≠ 0

Answer 1

Correct option is B. x + y, x ≠ 0

First of all we need to check the condition on x

If x = 0 then sec²x attains to infinity, so that condition must be true i. e x should not be zero Again if x + y =0 then the RHS part becomes infinity so that condition must be true i.e. x + y should not be zero.