in a right triangle abc with angle a equal to 90 degrees, find angle b and c so that sin(b) = cos(b).

Oh, this is easy love :)

So,  b is the length of the side opposite angle B and c is the length of the side opposite angle C and h is the length of the hypotenuse. 

sin(B) = b/h and cos(B) = c/h 

sin(B) = cos(B) means b/h = c/h which gives c = b 

The two sides are equal in length which means that the triangle is isosceles and angles B and C are equal in size of 45 degrees!

I hope this helps!

Right, so, angles B and C are equal in size of 45 degrees.

HTH :)