A common mistake would be to apply distributive property to make it cos 90 - cos theta. However, this is not applicable because these are trigonometric functions. Similarly, you need to apply trigonometric identities/properties
cos(A - B) = cosAcosB + sinaAsinB
In analogy,
cos (90 - ∅) = cos90*cos∅ + sin90*sin∅
Since cos 90 = 0; sin 90 = 1,
cos (90 - ∅) = sin∅
