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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