for positive acute angles A and B, it is known that cos A=9/41 and tan B=21/20. Find the value of sin(A+B) in simplest form.

Step-by-step explanation:

I attached a pic so you can see what the angles look like when you draw them out and construct right triangles out of them. We need to find the missing side lengths, ?, in each triangle. For A:

and

x = 40 For B:

and

x = 29. Now that we know all the sides of each triangle, we will use the sum identity for sin:

sin(A + B) = sinAcosB + cosAsinB. Filling in what we found in our triangles for each ratio: sin A = 40/41, sin B = 21/29, and cos B = 20/29

sin(A + B) = which simplifies to

And that's it. It doesn't simplify any further.