(i) To prove:- sin 2A =

A = 30°

∴ To show:- sin 60° =

Consider L.H.S. = =

=

= =

= √3/2

= sin 60° = R.H.S.

∴ R.H.S. = L.H.S.

Hence, verified.

(ii) To show:- cos 2A =

A = 30°

∴ To show:- cos 60° =

Consider R.H.S. = =

= 2/4 = 1/2 = cos 60° = L.H.S.

∴ R.H.S. = L.H.S.

Hence, verified.

(iii) To show:- tan2A =

A = 30°

∴ To show:- tan 60° =

Consider R.H.S. = = =

= 3/√3 = √3

= tan 60° = L.H.S.

∴ R.H.S. = L.H.S.

Hence, verified.