Question

Find a solution for the equation. assume that all angles are acute angles. sin( 2β + 10°) = cos( 3β - 25°)

Answer 1

The sine of one acute angle is equal to the cosine of another when their sum is 90°.
.. (2β +10°) +(3β -25°) = 90°
.. 5β -15° = 90°
.. 5β = 105°
.. β = 21°

Then your equation becomes
.. sin(52°) = cos(38°)