Question

Please answer fast best answer will be marked step wise explaination is needed

Answer 1

sin(θ/2) = 1/√3

=> cos(θ/2) = √(1-(1/√3)²) = √(1-1/3) = √(2/3)

so,

a) sinθ = 2.sin(θ/2).cos(θ/2)

           = 2 . 1/√3 . √(2/3) = 2√2 / 3

b)cosθ = 2.cos²(θ/2) - 1

           = 2.2/3 - 1 = 1/3

c)tanθ = sinθ/cosθ = 2√2

d)sin2θ = 2.sinθ.cosθ

             = 2.(2√2/3).(1/3) = 4√2 / 9

e)cos2θ = 2.cos²θ - 1

             = 2.1/9 - 1 = -7/9

f)tan2θ = sin2θ/cos2θ = -4√2/7