Question

Plzz solve it with full process..​

Answer 1

Answer:

see the attachment

Answer 2

Step-by-step explanation:

since cos(45)=1/√2 , sin(45)=1/√2, cos(-45)=1/√2, sin(-45)= -1/√2

Hence the equation can be written using Euler's form

as cos(α) + isin(α) = $e^{i\alpha }$

(1/√2 + i*1/√2) = $e^{i45}$

(1/√2 - i*1/√2) = $e^{-i45}$

hence

$(e^{i45})^{10} + (e^{-i45})^{10}$

now 45° can be written as  $\pi /4$

hence

=> $(e^{i\pi/4 })^{10} + (e^{-i\pi/4 })^{10}$

=> $(e^{i10\pi/4 }) + (e^{-i10\pi/4 })$                 as     $(x^{a})^{b} = x^{ab}$

=> $(e^{i5\pi/2 }) + (e^{-i5\pi/2 })$

change this into cos and sin

=> $cos(5\pi/2) + isin(5\pi/2) + cos(5\pi/2) - isin(5\pi/2)$

=> $2cos(5\pi/2)$

=> $2cos(2\pi + \pi/2)$

=> $2cos(\pi/2)$

=> 0

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