What is the value of cosec `(13pi//12)`?

Options

A. `sqrt(6)+sqrt(2)`
B. `-sqrt(6)+sqrt(2)`
C. `sqrt(2)-sqrt(2)`
D. `-sqrt(6)-sqrt(2)`

Answer

D

Explanation

`"cosec"((13pi)/(12))="cosec"(pi+(pi)/(12))`
`=-"cosec"(pi)/(12) =-"cosec"15^(@)`
`=-sqrt(1+cot^(2)15^(@))`
`=-sqrt(1+(2+sqrt(3))^(2)) " " [becausecot15^(@)=2+sqrt(3)]`
`=-sqrt(1+4+3+4sqrt(3))`
`=-sqrt(8+4sqrt(3))=-sqrt(6+2+2sqrt(12))`
`=-sqrt((6)^(2)+(sqrt(2))2(sqrt(6))(sqrt(2)))`
`=-sqrt((sqrt(6)+sqrt(2))^(2))=-sqrt(6)-sqrt(2)`