`sec^(2)theta==(4ab)/((a+b)^(2)),` where a, b `inR` is true if and olny if

Options

A. `a+b ne0`
B. `a=b, a ne0`
C. `a=b`
D. `a ne 0, bne0`

Answer

B

Explanation

We known that `sec ^(2)thetage1`
`therefore sec^(2)theta=(4ab)/((a+b)^(2))`
`impliesa,b ne0and-(4ab)/((a+b)^(2))ge1`
`impliesa,b ne0and (4ab)/((a+b)^(2))-1ge0`
`impliesa,b ne0and-((a-b)^(2))/((a+b)^(2))ge0`
`impliesa,b ne0and -(a-b)^(2)ge0`
`impliesa, b ne0and (a-b)^(2)le0impliesa =b and a ne0`