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(105Β°) = (β3/2)(β2/2) + (1/2)(β2/2)
sin(105Β°) = (β6 + β2)/4
Therefore, the answer is D, β6 + β2.
Given that sin(π΄ + π΅) = sin π΄ cosπ΅ +
cos π΄ sinπ΅, find the value of sin 105 Β°.
A. β42 (β3 + 1)
B. β42 (β3 β 1)
C. β42 (1 β β3)
D. β6 + β2
1 answer