Answer:
The sum sin30+cos60 is different to the sum sin60+cos30.
Explanation:
In order to find out how one of the sums will relate to the other, you can use the fact that the angles 30 and 60 are complementary angles because they add up to 90 degrees. In other words, the sum of them make a right angle.
When two angles (Let α and β represent them) are complementary, sin(α)=cos(β) and cos(α)=sin(β)
Therefore, in this case:
sin(30)=cos(60) (I)
cos(30)=sin(60) (II)
Replacing (I) in sin(30)+cos(60)
cos(60)+cos(60) = 2cos(60)
Replacing (II) in sin(60)+cos(30)
cos(30)+cos(30)=2cos(30)
Therefore, 2cos(60) ≠ 2cos(30) so the sums are different.