Use the halfformulas to find the exact value of the trigonom

Use the half-formulas to find the exact value of the trigonometric function sin 105 degrees. (Please show all steps and thank you in advance.)

Solution

sin(105)

1- 2sin^2x = cos2x

sinx = sqrt{ ( 1-cos2x)/2}

sin105 = sqrt{ (1-cos210)/2 }

cos210 = cos 180 +30) = -cos30 = -sqrt3/2

sin105 = sqrt { (1 +sqrt3/2)/2

= sqrt { ( 2 +sqrt(3)/4}

=sqrt { ( 2 +sqrt(3)} /2