`15^@` Find the exact values of the sine, cosine, and tangent of the angle.

You need to find the values of the sine, cosine and tangent of `15^o, ` such that:

`sin 15^o = sin ((30^o)/2) = sqrt((1 - cos 30^o)/2)`

`sin 15^o = sqrt((2 - sqrt 3)/4)`

`sin 15^o = (sqrt(2 - sqrt 3))/2`

`cos 15^o = cos ((30^o)/2) = sqrt((1 + cos 30^o)/2)`

`cos 15^o = (sqrt(2 + sqrt 3))/2`

`tan 15^o = (sin 15^o )/(cos 15^o)`

`tan 15^o = ((sqrt(2 - sqrt 3))/2)/((sqrt(2 + sqrt 3))/2)`

...

You need to find the values of the sine, cosine and tangent of `15^o, ` such that:

`sin 15^o = sin ((30^o)/2) = sqrt((1 - cos 30^o)/2)`

`sin 15^o = sqrt((2 - sqrt 3)/4)`

`sin 15^o = (sqrt(2 - sqrt 3))/2`

`cos 15^o = cos ((30^o)/2) = sqrt((1 + cos 30^o)/2)`

`cos 15^o = (sqrt(2 + sqrt 3))/2`

`tan 15^o = (sin 15^o )/(cos 15^o)`

`tan 15^o = ((sqrt(2 - sqrt 3))/2)/((sqrt(2 + sqrt 3))/2)`

`tan 15^o = ((sqrt(2 - sqrt 3)))/((sqrt(2 + sqrt 3)))`

`tan 15^o = ((sqrt(4 - 3)))/(2 + sqrt 3)`

`tan 15^o = 1/(2 + sqrt 3)`

`tan 15^o = 1/(2 + sqrt 3)`

`tan 15^o = (2 - sqrt 3)/(4-3)`

`tan 15^o = (2 - sqrt 3)`

Hence, evaluating the values of sine, cosine and tangent of `15^o` , yields `sin 15^o = (sqrt(2 - sqrt 3))/2, cos 15^o = (sqrt(2 + sqrt 3))/2, tan 15^o = (2 - sqrt 3).`