Find the exact value algebraically.

Question

Find the exact value algebraically of sin(105°)

Answer 1

sin(A+B)=sinAcosB + cosAsinB

sin(105) = sin(60+45) = sin60cos45 + cos60sin45 = 

[(√3)/2][(√2/2)] + (1/2)[(√2)/2] = 

(√6)/4 + (√2)/4 = (√6 + √2)/4