Question

If θ = 30°, verify tha:t

(i) sin 2 θ = 2 sin θ cos θ

(ii) cos 2 θ = 2 cos² θ - 1​

Answer 1

(i) sin2θ= 2sinθcosθ

sin2(30°)= 2sin30°cos30°

sin60°=2sin30°cos30°

√3/2=2×1/2×√3/2

√3/2=√3/2

L.H.S.=R.H.S

Hence verified

(ii) cos 2 θ = 2 cos² θ - 1

cos 2(30°) = 2 cos² 30° - 1

cos 60° = 2 cos² 30° - 1

1/2= 2×(√3/2)²-1

1/2= 2×3/4-1

1/2=3/2-1

1/2=1/2

L.H.S.=R.H.S

Hence verified

Answer 2

Answer:

i)(√3)/2=(√3)/2

ii) 1/2=1/2

Step-by-step explanation:

i)θ = 30°

sin2(30°)=2(sin(30°))(cos(30°))

sin60°=2×sin30°×cos30°

(√3)/2=2×1/2×√3/2

(√3)/2=(√3)/2

hence verified

ii) cos2(30°)=2cos^(2)30°-1

cos60°=2(1+cos2(30°))/2-1

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

1/2=1+1/2-1

1/2=1/2

hence verified