(i) To verify: sin (A - B) = sin A cos B - cos A sin B

If A = 60° and B = 30°, then

To verify: sin 30° = sin 60° cos 30° - cos 60° sin 30°

Consider R.H.S. = sin 60° cos 30° - cos 60° sin 30°

= (√3/2) × (√3/2) - (1/2) (1/2)

= (3/4) - (1/4)

= 2/4

=1/2

Consider L.H.S. = sin 30° = 1/2

∴ L.H.S. = R.H.S.

Hence, verified.

(ii) To verify: cos (A - B) = cos A cos B + sin A sin B

If A = 60° and B = 30°, then

To verify: cos (30°) = cos 60° cos 30° + sin60° sin 30°

Consider R.H.S. = cos 60° cos 30° + sin 60° sin 30°

= (1/2) × (√3/2) + (√3/2)(1/2)

= (√3/4) + (√3/4)

= √3/2 = cos 30° = L.H.S.

∴ L.H.S. = R.H.S.

Hence, verified.

(iii) To verify:- tan(A +B) =

If A = 60° and B = 30°, then

To verify: tan 90° =

Consider R.H.S. = =

= = 4/0 = ∞

= tan 90° = L.H.S.

∴ R.H.S. = L.H.S.

Hence, verified.