1.

If x,y,z are variables and `3tan x+4tany+5tanz=20,` then the minimum value of `tan^(2)x+tan^(2)y+tan^(2)z,` isA. 10B. 15C. 8D. 12

Answer» Correct Answer - C
`Let veca=3hati+4hatj+5hatk`
and, `hatb=(tanx)hati+(tany)hatk+(tanz)hatk.` Then,
`(veca,vecb)^(2)le|veca|^(2)|vecb|^(2)`
`implies(3tanx+4tany+5tanz)^(2)`
`" "le(9+16+25)(tan^(2)x+tan^(2)y+tan^(2)z)`
`implies(20)^(2)le50(tan^(2)x+tan^(2)y+tan^(2)z)`
`impliestan^(2)x+tan^(2)y+tan^(2)zge8`


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