Answer :
i. 
sin 12x + sin 4x
= 2 sin 8x cos 4x
ii. 
sin 5x – sin x
= 2 cos 3x sin 2x
iii. 
cos 12x + cos 8x
= 2 cos 10x cos 2x
iv. sin 2x + cos 4x
= sin 2x + sin (90° - 4x)
= 2 sin (45° - x) cos (3x – 45°)
= 2 sin (45° - x) cos {-(45° - 3x)}
{cos (-x) = cos x}
= 2 sin (45° - x) cos (45° - 3x)
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