Use trigonometric identities to calcuate sin(345)

We have to find sin 345.

sin
345 = sin ( 360 - 15) = - sin 15

Now cos 30 = (cos 15)^2 -
( sin 15)^2

=> cos 30 = 1 - 2*(sin
15)^2

=> 1 - 2*(sin 15)^2 = cos
30

=> - 2*(sin 15)^2 = cos 30 -
1

=> 2 (sin 15)^2 = 1 - cos
30

=> 2 (sin 15)^2 = 1 - sqrt
3/2

=>  (sin 15)^2 = 1/2 - sqrt
3/4

=> (sin 15) = sqrt (1/2 - sqrt
3/4)

=> sin 15 = sqrt (1/2 - sqrt
3/4)

Therefore sin 345 = - (sqrt (1/2 - sqrt
3/4))