I need the explanation for the prove that sinx + icosx = 1
where i is imaginary unit.

Prectega:
I need the explanation for the prove that
sinx + icosx = 1

where i is imaginary unit.

We can solve using euler's formular:

e^ix = cosx + isinx
Where
Cosx= re(e^ix)= 1/2 e^ix + 1/2 e^-ix
And sinx= lm(e^ix)= -1/2 e^ix + 1/2 e^-ix
So let sinx + icosx =Y where Re means real and Im means immaginary.
Substituting for Cosx and sinx into the equation sinx + icosx = Y we have,
Y= (- 1/2 e^ix + 1/2 e^-ix) + i(1/2 e^ix + 1/2 e^-ix)
Collecting like terms we have,
Y =(1/2 e^ix - 1/2 e^ix) +(1/2 e^-ix +1/2 e^-ix)
We have
Y= 0 + 2(-1/2 e^-ix)
Y=-e^-ix
Y= 1
Hence y= sinx + icosx =-e^-ix= 1.

To be sincere I was once d best in math 305 in d university. I could prove that with my materials and diary point jot. But I graduated 2 years ago.

Dnt knw how to help,but I believe some nairalanders would help out. At last I remembered

i use to like maths until they started including alphabets ;Di use to like maths until they started including alphabets

Taking magnitude of the equation will give one i.e (sin^2)x + (cos^2)x

Prove