Question

Express $\frac{{(cos\theta +isin\theta )}^4}{{i(cos\theta +isin\theta )}^{-4}}$ in a + ib form.

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

Base of the numerator and denominator is same.

Denominator can bring to the numerator with change in sign of power.

$\frac{1}{i}$ $(cos\theta +isin\theta {)}^4$$(cos\theta +isin\theta {)}^4$

=$\frac{1}{i}$ $(cos\theta +isin\theta {)}^8$

=$\frac{1}{i}$$[cos8\theta +isin8\theta ]$

=$sin8\theta -icos8\theta$