if-z-C-is-sin-2-z-cos-2-z-1-also-valid-

Question Number 75655 by mr W last updated on 15/Dec/19

i f z \in C

i s \sin^{2} z + \cos^{2} z = 1 a l s o v a l i d ?

Answered by MJS last updated on 15/Dec/19

yes .

\sin^{2} z = {(\frac{e^{i z} - e^{- i z}}{2 i})}^{2} = \frac{e^{2 i z} - 2 + e^{- 2 i z}}{- 4}

\cos^{2} z = {(\frac{e^{i z} + e^{- i z}}{2})}^{2} = \frac{e^{2 i z} + 2 + e^{- 2 i z}}{4}

\frac{e^{2 i z} - 2 + e^{- 2 i z}}{- 4} + \frac{e^{2 i z} + 2 + e^{- 2 i z}}{4} = 1

Commented by mr W last updated on 15/Dec/19

t h a n k y o u f o r c o m f i r m i n g, s i r .

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