JEE Main20202 Sep 2020Morning ShiftMathematicsComplex NumberActual
The value of 1 + sin 2 π 9 + i cos 2 π 9 1 + sin 2 π 9 − i cos 2 π 9 3 is
Options
- A1 2 ( 1 - i 3 )
- B1 2 ( 3 - i )
- C- 1 2 ( 3 - i )
- D− 1 2 1 − i 3
Correct answer
C. - 1 2 ( 3 - i )
Step-by-step solution
1 + sin 2 π 9 + i cos 2 π 9 1 + sin 2 π 9 − i cos 2 π 9 3 = 1 + cos 5 π 18 + i sin 5 π 18 1 + cos 5 π 18 - i sin 5 π 18 3 = 2 cos 2 5 π 36 + i 2 sin 5 π 36 · cos 5 π 36 2 cos 2 5 π 36 - i 2 sin 5 π 36 · cos 5 π 36 3 = cos 5 π 36 + i sin 5 π 36 cos 5 π 36 - i sin 5 π 36 3 = cos 5 π 36 + i sin 5 π 36 6 = cos 6 × 5 π 36 + i sin 6 × 5 π 36 = cos 5 π 6 + i sin 5 π 6 = - 3 2 +