Question

Given that sin(𝐴 + 𝐵) = sin 𝐴 cos𝐵 +
cos 𝐴 sin𝐵, find the value of sin 105 °.
A. √42 (√3 + 1)
B. √42 (√3 − 1)
C. √42 (1 − √3)
D. √6 + √2

Answer 1

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

sin(60° + 45°) = sin60°cos45° + cos60°sin45°

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.