Express each of the following as the product of sines and cosines: i. sin 12x + sin 4x ii. sin 5x – sin x iii. cos 12x + cos 8x iv. sin 2x + cos 4x

Question

Philoid · Accepted 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)