if cot theta= 1/ root 3, show that 1-cos square theta/ 2- sin square theta = 3/5 - Maths - Introduction to Trigonometry

Question

if cot theta= 1/ root 3, show that 1-cos square theta/ 2- sin
square theta = 3/5

Stunning Dude....... · Accepted Answer

let theta = x
cot x = 1/root3
cot x = cot 60
x = 60 degree
now,
1 - cos2x / 2 - sin2x = 3/5
1 - (cos 60)2 / 2 - (sin 60)2 = 3/5
1 - (1/2)2 / 2 - (root3/2)2 = 3/5
1 - 1/4 / 2 - 3/4 = 3/5
(3/4) / (5/4) = 3/5
3/5 = 3/5
HENCE PROVED

if cot theta= 1/ root 3, show that 1-cos square theta/ 2- sin square theta = 3/5.