evaluate the following.
(iii) sin 30° + tan 40° - cosec 60° / cot 45° + cos 60° - sec 30°

Sin 30 = 1/2
tan 45 = 1
Cosec 60 = 2 / √3 = 2√3 / 3
cot 45 = 1
Cos 60 = 1/2
sec 30 = 2 / √3 = 2√3 / 3
_______________________________
[ 1/2 + 1 - 2√3/3 ] ÷ [ 1 + 1/2 - 2√3/3 ] = 1
The face and denominator of the fraction are exactly the same thus the answer is 1 .