Given that `a , b , c ,` are the side of a ` A B C` which is right angled at `C ,` then the minimum value of `(c/a+c/b)^2` is 0 (b) 4 (c) 6 (d) 8

Options

A. 0
B. 4
C. 6
D. 8

Answer

D

Explanation

`a=c sin theta, b=c cos tehta`
`rArr ((c)/(a)+(c)/(b))^(2)=((1)/(sin theta)+(1)/(cos theta))^(2)=(4(1+sin2theta))/(sin^(2)2theta)`
`=4((1)/(sin^(2)2theta)+(1)/(sin 2theta))`. Where `0ltthetalt(pi)/(2)`
`rArr ((c)/(a)+(c)/(b))^(2)=8`, when `2theta=90^(@)`.