Question

Use trigonometric identities to find exact trigonometric function values. Find the exact value of tan(-π/12)

Answer 1

`√(3) -2`

Explanation:

`\boxed{tan((\theta)/(2) )=(1-cos\theta)/(sin\theta) }`

`tan(-(\pi)/(12) )=tan((1)/(2)( -(\pi)/(6) ))`

`=(1-cos(-(\pi)/(6) ))/(sin(-(\pi)/(6)) )`

`=(1-(1)/(2)√(3) )/(-(1)/(2) )`

`=-2(1-(1)/(2) √(3) )`

`=√(3) -2`