Came up with a second personalized proof (is it correct)

[Miike012]

.....

 

[Miike012]

proof of sin(90 + theta) = cos(theta)

 

[HallsofIvy]

Well, I wouldn't say "by construction angle COD is also theta". Since OD is perpendicular to AE, the only thing that is true "by construction" is that angle ODE and ODA are right angles. Now, you can they show that COD is theta by using the fact that the two angles in a right triangle are complementary- but you should show that.

 

[praharmitra]

Wait. Am I missing something here. Shouldn't COD be 45-(theta/2) ?

AOE is an isosceles triangle. The perpendicular is also the angle bisector, right? Or have I understoond something wrong here?

 

[Miike012]

Sorry.. after I looked at it... segment OD is not perp to segment AE.. and it doesn't have to be. I came up with a diff steps which I edited in the picture that I attached..