Question

Question #b9c5a

Answer 1

Given
`cosecA=2/sqrt3`
`=>cosecA=cosec(pi/3)=cosec(pi-pi/3)`
(Takling `2pi>A>0`)

`"So "A =pi/3 or (2pi)/3`

So `tanA=tanpi/3=sqrt3`

or `tanA=tan(2pi)/3=tan(pi-pi/3)`
`=-tanpi/3=-sqrt3`

Alternative

Given
`cosecA=2/sqrt3`

`=>(cosecA)^2=(2/sqrt3)^2`

`=>cosec^2A=4/3`

`=>1+cot^2A=4/3`

`=>cot^2A=4/3-1=1/3`

`=>tan^2A=3`

`=>tanA=+-sqrt3`

Given
`cosecA=+ve->` A lying in 1st or 2nd quadrant.
When A is in 1st quadrant then `tanA =sqrt3`

When A is in 2nd quadrant then `tanA =-sqrt3`