Question

Given that sin α = √3/2 and tan β = 1/√3, then the value of cos (α - β) is :

(a) √3/2

(b) 1/2

(c) 0

(d) 1/√2

Answer 1

Correct answer is (a) √3/2

Given,

sin α = √3/2

sin α = sin 60°

α = 60°

tan β = 1/√3

tan β = tan 30°

β = 30°

∴ cos (α - β)

= cos (60° - 30°)

= cos 30°

= √3/2

Answer 2

GIVEN:

sin ɑ  =  √3 / 2

sin ɑ  =  sin 60°  [Standard value of ratios]

ɑ  =  60°

tan β  =  1/√3

tan β  =  tan 30°  [Standard value of ratios]

β  =  30°

So,

cos (ɑ - β)

=  cos (60 - 30)

= cos 30°

=  √3 / 2

Hence, the correct answer is :

(A) √3 / 2