(i) sin 3x = 3 sin x – 4 sin3 x
L.H.S. = sin 3x
= sin 3 × 30° [∵ Given x = 30°]
= sin 90°
= 1
R.H.S. = 3 sin x – 4 sin3 x
= 3sin 30° – 4 sin3 30°
Thus, L.H.S. = R.H.S.
(ii) tan2x = 2tanx/(1 - tan2x)
L.H.S. = tan 2x
= tan 2 × 30° [∵ Given x = 30°]
= tan 60° = √3
R.H.S. = 2tanx/(1 - tan2x)
∴ L.H.S. = R.H.S.
(iii) sinx = √((1 - cos2x)/2)
∴ L.H.S. = R.H.S.
(iv) cos 3x = 4 cos3 x – 3 cos x
L.H.S. = cos 3x = cos 3 × 30°
= cos 90°
= 0 [∵ Given x = 30°]
R.H.S. = 4 cos3 x – 3 cos x
= 4 cos3 30° – 3 cos 30°
L.H.S. = R.H.S.