Given that sin(𝐴 + 𝐡) = sin 𝐴 cos𝐡 +

cos 𝐴 sin𝐡, find the value of sin 105 °.
A. √42 (√3 + 1)
B. √42 (√3 βˆ’ 1)
C. √42 (1 βˆ’ √3)
D. √6 + √2

1 answer

We know that sin(A+B) = sinAcosB + cosAsinB. We can use this formula for A = 60Β° and B = 45Β° as follows:

sin(60Β° + 45Β°) = sin60Β°cos45Β° + cos60Β°sin45Β°

Simplifying using known values:

sin(105°) = (√3/2)(√2/2) + (1/2)(√2/2)

sin(105°) = (√6 + √2)/4

Therefore, the answer is D, √6 + √2.