SOLUTION: how do i verify the identity of sin(x+pi/2)=cos x

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Question 1149958: how do i verify the identity of sin(x+pi/2)=cos x
Found 3 solutions by Alan3354, Edwin McCravy, ikleyn:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
how do i verify the identity of sin(x+pi/2)=cos x
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Use sin(A + B)
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If you don't know that, look at "Half angle formulas" on Wikipedia
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!
Use the formula 

on the left side:









Edwin
Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.

Apply the addition formula for sine


    sin(a+b) - sin(a)*cos(b) + cos(a)*sin(b).     (1)


It is one of the basic formula of Trigonometry; it is valid for all angles  "a" and  "b".


Put  a = x  and  b = .  You will get


     =  + .    (2)


Take into account that    = 0,    = 1.

Then you can continue the line (2) in this way


          =  +  = sin(x)*0 + cos(x)*1 = cos(x).


Thus the identity   = =cos x  is proved for all angles  x.

Solved, explained and completed.


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