What is the value of `sin((5pi)/(12))`?

Options

A. `(sqrt(3)+1)/(2)`
B. `(sqrt(6)+sqrt(2))/(4)`
C. `(sqrt(3)+sqrt(2))/(4)`
D. `(sqrt(6)+1)/(2)`

Answer

B

Explanation

`"sin"(5pi)/(12)=sin75^(@)`
`=sin(45^(@)+30^(@))`
`=sin45^(@)cos30^(@)+cos45^(@)sin30^(@)`
`=(1)/(sqrt(2))*(sqrt(3))/(2)+(1)/(sqrt(2))*(1)/(2)=(1)/(sqrt(2))((sqrt(3)+1)/(2))`
`=(sqrt(3)+1)/(2sqrt(2))xx(sqrt(2))/(sqrt(2))=(sqrt(6)+sqrt(2))/(4)`