250121If sin(α+β)=1, α=60°, then the value of [cos(α-β)/cosβ]2 = _______

Question: If sin(α+β)=1, α=60°, then the value of [cos(α-β)/cosβ]² = ________

a) 0
b) 1/2
c) (√3)/2
d) 1

Doubt by Muskan 

Solution:

sin(α+β)=1
sin(α+β)=sin90°
α+β=90°
60°+β=90° [∵ α=60°]
β=90°-60°
β=30°

Now,
=[cos(60°-30°)/cos30°]²
=[cos(30°)/cos30°]²
=[1]²
=1

∴ d) is the correct option.