Question 130116
If you draw a picture, you'll notice that angle A and B are connected. If you know the measure of angle A, then angle B is: B=90-A

So

{{{sin (A) - cos (B)}}}

also looks like

{{{sin (A) - cos (90-A)}}}

Now if you look at the list of identities, you'll see one that reads: *[Tex \LARGE \sin\left(\theta\right)=\cos\left(90-\theta\right)]

So our expression becomes

{{{sin (A) - sin (A)}}} Just replace {{{cos (90-A)}}} with {{{sin(A)}}}

and the expression evaluates to 0

So

{{{sin (A) - cos (B)=0}}}