Question

show that 1 minus sin 60 degree by Cos 60 degree = tan 60 degree minus 1 by tan 60 degree + 1​

Answer 1

(1 - sin 60)/cos 60 = (tan 60 - 1)/(tan 60 + 1) ——> 1

We know that

sin 60 = sqrt(3)/2 ——> 2

cos 60 = 1/2 ——> 3

tan 60 = sqrt(3) ——> 4

Substitute 2, 3 & 4 in equation 1,

(1-(sqrt(3)/2))/(1/2) = (sqrt(3) - 1)/(sqrt(3) + 1)

(2 - sqrt(3)) = ((sqrt(3) - 1)*(sqrt(3) - 1))/((sqrt(3) + 1)* (sqrt(3) - 1))

(2 - sqrt(3)) = (sqrt(3) - 1)^2/((sqrt(3) + 1)* (sqrt(3) - 1))

(2 - sqrt(3)) = (sqrt(3) - 1)^2/(3 - 1)

(2 - sqrt(3)) = (3 + 1 - 2*sqrt(3)*1)/(2)

(2 - sqrt(3)) = (4 - 2*sqrt(3))/(2)

(2 - sqrt(3)) = 2*(2 - sqrt(3))/(2)

(2 - sqrt(3)) = (2 - sqrt(3))

L. H. S = R. H. S

Hence Proved