Does anyone understand this answer? proving sin(A-B)

[eeuler]

I had no clue how to do this and could only grasp the first basic parts but even then i couldn't get it right and in the end i had to look at the answer, which confused me even more. So i was wondering if anyone else understands this, and if so could you describe it in words please?

Homework Statement

Homework Equations

As above

The Attempt at a Solution

I understand the first part, getting cos B from the graph...yet when it gets to the other part '...angle in the bottom right hand corner of the triangle is PI - A...' i don't understand how they came to that...but i was wondering, the sin (PI/2 - A) seems to be related to a trigonometric identity? If someone could explain it that would be great.

 

[HallsofIvy]

I had no clue how to do this and could only grasp the first basic parts but even then i couldn't get it right and in the end i had to look at the answer, which confused me even more. So i was wondering if anyone else understands this, and if so could you describe it in words please?

Homework Statement

Homework Equations

As above

The Attempt at a Solution

I understand the first part, getting cos B from the graph...yet when it gets to the other part '...angle in the bottom right hand corner of the triangle is PI - A...' i don't understand how they came to that...but i was wondering, the sin (PI/2 - A) seems to be related to a trigonometric identity? If someone could explain it that would be great.

The angle in the bottom right hand corner is NOT $\pi- A$. The two non-right angles in a right triangle must add to $\pi/2$. Since the whole angle in the upper left is A, the angle in the bottom righthand corner is $\pi/2- A$.

 

[eeuler]

Thank you for that, it clears some of the confusion, thanks.