Given that sin(5x-28)degree=cos(3x-5),0 lessthan x lessthan 90degree,find the value of x.

Answer 1

If sin A = cos B, A and B must be complementary angles (if both are less than 90 degrees).
That means
5x - 28 + 3x -5 = 90 degrees
8x = 123
x = 15.375 degrees
Check: sin (5x-28) = sin 48.875 = 0.753276
cos (3x-5) = cos 41.125 = 0.753276

There might be other solutions for which 5x-28 exceeds 90 degrees. Check it out