`Tan 75 - Cot 75=`

Options

A. `2sqrt(3)`
B. `2+sqrt(3)`
C. `2-sqrt(3)`
D. 1

Answer

A

Explanation

Given expression, `tan75^(@)-cot75^(@)`
`" "=(sin75^(@))/(cos75^(@))-(cos75^(@))/(sin75^(@))`
`" "=(sin^(2)75^(@)-cos^(2)75^(@))/(sin75^(@)*cos75^(@))`
`" "=(-2cos150^(@))/(sin150^(@))`
`" "=(-2cos(90^(@)+60^(@)))/(sin(90^(@)+60^(@)))` ltBrgt `" "=(+2sin60^(@))/(cos60^(@))`
`" "=(2*(sqrt(3))/(2))/((1)/(2))=2sqrt(3)`