Question

Use the half-angle identity to find the exact value of sin 105 degrees.
Please help

Answer 1

Hello,

cos 2a=1-2sin²a==>2sin²a=1-cos2a

cos (105°*2)=-cos(30°)=-√3/2
==>2sin²105°=1+√3 /2=(2+√3)/2
==>sin²105°=(2+√3)/4
==>sin 105°=1/2*√(2+√3)