SOLUTION: sin theta = cos (theta - 30°) theta is +ve acute angle. Find sin theta + cos theta.

sinq = cos(q - 30°)

The word "cosine" is an abbreviation for "complement's sine"

If the sine of one positive acute angle equals the
cosine of another positive acute angle, then the
angles are complementary.  Therefore:

q + (q - 30°) = 90°

  q + q - 30° = 90°
    
     2q - 30° = 90°
 
           2q = 120°

            q = 60°  

sinq = 

cosq = 

sinq + cosq = .

Edwin