Question

Use de Moivre's formula to evaluate the power  (cos⁢2⁢+i⁢ sin2)-1 in Cartesian form.

Of these multiple choice, which is correct?

A.) cos 2 - i sin 2

B.) $\frac{1}{cos 2 - i sin 2}$

C.) $\frac{1}{cos 2}-i\frac{1}{sin 2}$

D.) $\frac{1}{cos 2}+i\frac{1}{sin 2}$

E.) cos 2 + i sin 2

Answer 1

De Moivre's formula (Cos (0) + i sin (0)" = cos (10) + i søn (leo) Using above Expression (cose + sin(2)) cos (-1(2))+ i sin(-1)(21) = cos(-2) + i sin (-2) = cos(2) - i sin (2) Option (A) is correct Answer We know that cos (-0) = coso Sint-o)=-Sino