ok this has been bugging me all day,

the answer should come out too

-2+√3

whenever i use the sum and difference identities for tan

i got (1-√3)/(1+√3)

then out of frustration i decided to find sin(-π/12)

which came out to (√2-√6)/4

then found cos(-π/12)

which came out to (√2+√6)/4

then i did sin(-π/12)/cos(-π/12)

which came out to

(√2-√6)/(√6+√2)

i know everything i have done is correct because when plugging into calculator with final answer, with all 3 answers

tan... (1-√3)/(1+√3)

sin/cos... (√2-√6)/(√6+√2)

and the final answer in back of book... -2+√3

they all came out with the same values... so my question question is...

how the heck do i reduce

(1-√3)/(1+√3)??

and why not how do i reduce

(√2-√6)/(√6+√2)??

to equal the final simplified version of -2+√3??????

thank you in advance