# How do you verify the identity #sin(pi/2 + x) = cosx#?

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#### Answer

#### Answer:

#### Explanation

#### Explanation:

for the "true" proof you need to use matrice, but this is acceptable :

So we have :

Since this answer is very usefull for student here the full demonstration to obtain

(do not read this if you are not fan of math)

a complex numbers can be written in trigonometrics form

multiplying

because

just for you to know, multiplying a complex numbers by

another way to do a 90° rotation is to derivate

we have

integrating both part

taking

so

multiplying by another complex number

develop

real part of left must be equal to real part of right idem for imaginary part

note :

because

#### Answer

#### Answer:

#### Explanation

#### Explanation:

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#### Answer:

If you want a simple conceptual way

(rather than a formal way)

Think about triangles

#### Explanation:

With

Let's say the angle opposite

Now, you probably know that there are

Therefore,

The right angle is

which means,........

Keep that in the back of your mind

Hopefully you can see why that is?

sub in our formula for

( which also means,

cos is an even function (meaning

so

or put in a better way,......

I hope this was a little more intuitive than diving into aspects of complex analysis.

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