Find the exact value by using a half-angle identity. sin(5pi/12)

Find tan(5π12) and sin ((5pi)/12)
 ±(2±√3)and±√2+√32

Explanation:

Call tan ((5pi/12) = t. 
Use trig identity: tan2a=2tana1−tan2a
tan(10π12)=tan(5π6)=−1√3=2t1−t2
t2−2√3t−1=0

D=d2=b2−4ac=12+4=16--> d=±4

t=tan(5π12)=2√32±42=2±√3

Call sin(5π12)=siny
Use trig identity: cos2a=1−2sin2a
cos(10π12)=cos(5π6)=−√32=1−2sin2y
sin2y=2+√34
siny=sin(5π12)=±√2+√32

Using the distributive property...you can multiply and add your way to an answer.

6.8(6.7 - 7.2) - 2(4.6 + 1.2)                      (use distributive property)
6.8(6.7) + 6.8(-7.2) - 2(4.6) - 2(1.2)            (multiply)
45.56 - 48.96 - 9.2 - 2.4                        (add)
- 15                                                         (answer)