If x,yz are variables and
`3tan x+4tany+5tanz=20,`
then the minimum value of `tan^(2)x+tan^(2)y+tan^(2)z,` is

Options

A. 10
B. 15
C. 8
D. 12

Answer

C

Explanation

We know that
`(a_(1)b_(1)+a_(2)b_(2)+a_(3)b_(3))^(2)le(a_(1)^(2)+a_(2)^(2)+a_(3)^(2))(b_(1)^(2)+b_(2)^(2)+b_(3)^(2))`
`:." "(3tanx+4tany+5tanz)^(2)`
`le(3^(2)+4^(2)+5^(2))xx(tan^(2)x+tan^(2)y+tan^(2)z)`
`implies" "(20)^(2)le50(tan^(2)x+tan^(2)y+tan^(2)z)`
`implies" "tan^(2)x+tan^(2)y+tan^(2)zge8.`