Let @ = cose + isin0, 0<0 <¹ 2 1 (a) (i) Show that " -= 2isin no, where ne *. n 5 (ii) Using the Binomial theorem, find

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Let Cose Isin0 0 0 2 1 A I Show That 2isin No Where Ne N 5 Ii Using The Binomial Theorem Find 1 (53.41 KiB) Viewed 29 times

complex number. Need clear steps. Thanks in advance.
Let @ = cose + isin0, 0<0 <¹ 2 1 (a) (i) Show that " -= 2isin no, where ne *. n 5 (ii) Using the Binomial theorem, find an expression for sin in the form 1 asin A + bsin BO + csin CO), where a, b, c, A, B and C are real. 16 (b) Given further that w5-1=0, (i) find the value of 0; (ii) show that 1+w+w² +³ +w¹ = 0; (iii) if 1,0,0²,0³ and ¹ are the roots of a polynomial f(x), show that 2π 4π f(x) = (x-1)(x² - 2cos- -x+1x²-2 cos- - (x+1). 5 5