Question 1036926
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Use the Angle sum identity to verify:

sin(x+(pi/2))=cos x
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<pre>
the Angle sum identity for sine is

{{{sin(alpha+beta)}}} = {{{sin(alpha)*cos(beta) + cos(alpha)*sin(beta)}}}

(see, for example, the lesson <A HREF=https://www.algebra.com/algebra/homework/Trigonometry-basics/Addition-and-subtraction-formulas.lesson>Addition and subtraction formulas</A> in this site).


Now apply it:

{{{sin(x+(pi/2))}}} = {{{sin(x)*cos(pi/2) + cos(x)*sin(pi/2)}}}.


Remind that  {{{cos(pi/2)}}} = 0  and  {{{sin(pi/2)}}} = 1. Then you can continue the line above as

= sin(x)*0 + cos(x)*1 = cos(x).
</pre>

Verified.