AP EAMCET202023 Sep 2020Morning ShiftMathematicsComplex NumberActual
1 + cos ( 3 θ ) + i sin ( 3 θ ) 1 + cos ( 3 θ ) - i sin ( 3 θ ) 20 = ?
Options
- Acos ( 60 θ ) + i sin ( 60 θ )
- Bcos ( 60 θ ) - i sin ( 60 θ )
- Ccos ( 20 θ ) + i sin ( 20 θ )
- Dcos ( 20 θ ) - i sin ( 20 θ )
Correct answer
A. cos ( 60 θ ) + i sin ( 60 θ )
Step-by-step solution
1 + cos 3 θ +   i   sin 3 θ 1 + cos 3 θ - i   sin 3 θ 20 = 2 cos 2 3 θ 2 + i 2 sin   3 θ 2 · cos 3 θ 2 2 cos 2 3 θ 2 - i 2 sin 3 θ 2 · cos 3 θ 2 20 = cos 3 θ 2 + i   sin 3 θ 2 cos 3 θ 2 -   i sin 3 θ 2 20 = e i 3 θ 2 e - i 3 θ 2 20 = ( e i 3 θ ) 20 = ( e i 60 θ ) = cos ( 60 θ ) + i   sin ( 60 θ )