help me in complex numbers

Salman91

Using De’Moivre’s Theorem, prove that

cos^4 θ= 1/8 cos4θ + 1/2 cos2θ+ 3/8

Kindly show the solution,

Thanks.

CaptainBlack

MHF Hall of Fame
Using De’Moivre’s Theorem, prove that

cos^4 θ= 1/8 cos4θ + 1/2 cos2θ+ 3/8

Kindly show the solution,

Thanks.
Show us what you have done, then we will explain any errors

CB

mr fantastic

CaptainBlack

MHF Hall of Fame

$$\displaystyle \displaystyle (\cos (\theta)+i \sin(\theta))^4= \cos(4\theta)+i\sin(4\theta)$$

Expand the left hand side and equate real parts on both sides of the resulting equation. Now it should be just an exercise in the repeated application of trig identities.

CB

Last edited:
mr fantastic

Prove It

MHF Helper
$$\displaystyle \displaystyle (\cos (\theta)+i \sin(\theta))^4= \cos(4\theta)+i\sin(\theta)$$
$$\displaystyle (\cos{\theta} + i\sin{\theta})^4 = \cos{(4\theta)} + i\sin{(4\theta)}$$.