Angles α and β are the two acute angles in a right triangle. use the relationship between sine and cosine to find the value of β if β < α. sin(7x − 15) = cos(3x + 5)

We know that
in a right triangle
if sin A= cos B
then
angle A and angle B are complementary angles
so A+B=90

therefore
(7x-15)+(3x+5)=90> 10x-10=90> 10x=100> x=10°
so
7x-15> 7*10-15> 55°
3x+5> 3*10+5> 35°

we know that
β < α
therefore

the answer is
β =35°
α=55°