SOLUTION: If angle A and angle B are acute angles of right triangle ABC, what is the value of sin A - cos B ?

Algebra ->  Triangles -> SOLUTION: If angle A and angle B are acute angles of right triangle ABC, what is the value of sin A - cos B ?      Log On


   

Question 130116: If angle A and angle B are acute angles of right triangle ABC, what is the value of sin A - cos B ?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
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+%28A%29+-+cos+%28B%29

also looks like

sin+%28A%29+-+cos+%2890-A%29

Now if you look at the list of identities, you'll see one that reads:



So our expression becomes

sin+%28A%29+-+sin+%28A%29 Just replace cos+%2890-A%29 with sin%28A%29


and the expression evaluates to 0


So

sin+%28A%29+-+cos+%28B%29=0