In order for the sine and cosine to be equal, the angles must be complementary
sin (7x-15) = cos (3x+5)
7x-15+3x+5 =90 (because sum of both angles a and b must be 90)
10x -10 = 90
10x = 100
x =10
One angle = 7x-15= 7*10-15 = 70-15 =55
Other angle = 3x +5 = 3*10+5 = 30+5 = 35
Since B is less than A, A = 55 degrees and B = 35 degrees
Since we need B, B = 35 degrees