Question

please help me to solve 8(a)(b), 13(a)(b), 3, 4! Please help me to solve all of them! Thanks a lot!

6, show that, for real θ, (a) tan θ = iter-e-TO) 7, show that ez-emri for all z. (The exponential function is periodic with period 2mi.) show that, for all z, (b) ee 9, show that (ez)" = enz for any integer n. 10. Show that lel s 1 if Rezs o. 11. Determine which of the following properties of the real exponential function remain true for the complex exponential function (that is, for x replaced by z). (a) er is never zero. (c) et is defined for all x. (b) e* is a one-to-one function. (d) ex1/e 12. Use De Moivre's formula together with the binomial formula to derive the following identities. (a) sin 3θ 3 cos2 θ sin θ-sin3 θ (b) sin 4θ= 4 cos3 θ sine-4 cos θ sin3 θ 3, Show how the following trigonometric identities follow from Eqs. (11) and (12). (a) sin2 θ+ cos2#21 (b) cos (81 +&z) = cosa cos θ2-sino, sin θ2

Answer 1

You have not provided any eqn that are required in question 13.

positive inrY 3 7 3 ナーし 2. sinc eTCoso con+isin(sino) ecos oCos (sin)-in(sino e.