If sin(A + B) = sinAcosB + cosAsinB, then the value of sin75° is:
Show answer & explanation
Correct answer: D
Explanation
Given:
sin(A + B) = sinAcosB + cosAsinB
sin75° = sin(45° + 30°)
By the formula:
sin(A + B) = sinAcosB + cosAsinB
sin75° = sin(45° + 30°)
= sin45°cos30° + cos45°sin30°
= (1/√2 × √3/2) + (1/√2 × 1/2)
= √3/(2√2) + 1/(2√2)
= (√3 + 1)/(2√2)