SOLUTION: I have a verbal exam question that confuses me. How would I prove that sin(x + Pi/2)=cos(x) and cos(pi/2)=-sin(x) and then use these proofs to prove that (cos(x))'=-sin(x), if w

Algebra ->  Trigonometry-basics -> SOLUTION: I have a verbal exam question that confuses me. How would I prove that sin(x + Pi/2)=cos(x) and cos(pi/2)=-sin(x) and then use these proofs to prove that (cos(x))'=-sin(x), if w      Log On


   

Question 1194018: I have a verbal exam question that confuses me.
How would I prove that sin(x + Pi/2)=cos(x) and cos(pi/2)=-sin(x) and then use these proofs to prove that (cos(x))'=-sin(x), if we assume that (sin(x))'=cos(x)?
I am at loss regarding how I should create this collected explanation.
I would love any help sent my way.
Kind regards
Answer by Solver92311(821) About Me  (Show Source):
You can put this solution on YOUR website!

You misstated your problem: You want to prove

Use the addition formulas:





To prove both and

Then

Use the chain rule: Let



from the assumption, then



John

My calculator said it, I believe it, that settles it

From
I > Ø