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Question Number 68021 by anaplak last updated on 03/Sep/19

Commented by Tanmay chaudhury last updated on 03/Sep/19

	Answered by Tanmay chaudhury last updated on 03/Sep/19

	$p - 1 = \frac{1}{2} c o s 2 α - \frac{1}{2.4} c o s 4 α + \frac{1.3}{2.4.6} c o s 6 α + . . .$ $q = \frac{1}{2} s i n 2 α - \frac{1}{2.4} s i n 4 α + \frac{1.3}{2.4.6} s i n 6 α + . . .$ $(p - 1) + i q = \frac{1}{2} e^{i 2 α} - \frac{1}{2.4} e^{i 4 α} + \frac{1.3}{2.4.6} e^{i 6 α} - . . .$ $p + i q = 1 + \frac{1}{2} e^{i 2 α} - \frac{1}{2.4} e^{i 4 α} + \frac{1.3}{2.4.6} e^{i 6 α} - . . .$ $p + i q = {(1 + e^{i 2 α})}^{\frac{1}{2}} = {(1 + c o s 2 α + i s i n 2 α)}^{\frac{1}{2}}$ $p + i q = {[2 {c o s}^{2} α + i 2 s i n α c o s α]}^{\frac{1}{2}}$ $p + i q = {[2 c o s α (e^{i α})]}^{\frac{1}{2}}$ $p + i q = 2^{\frac{1}{2}} {(c o s α)}^{\frac{1}{2}} e^{i \times \frac{α}{2}}$ $p + i q = 2^{\frac{1}{2}} {(c o s α)}^{\frac{1}{2}} (c o s \frac{α}{2} + i s i n \frac{α}{2})$ $s o p = 2^{\frac{1}{2}} . {(c o s α)}^{\frac{1}{2}} . c o s \frac{α}{2}$ $q = 2^{\frac{1}{2}} . {(c o s α)}^{\frac{1}{2}} . s i n \frac{α}{2}$ $p l s c h e c k . . .$
	Commented by mathmax by abdo last updated on 03/Sep/19

	$s i r T a n m a y y o u h a v e u s e d r e l a t i o n 20.12 y o u a n s w e r i s c o r r e c t .$
	Commented by Tanmay chaudhury last updated on 03/Sep/19

	$t h a n k y o u s i r . . .$
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