Anyone can establish and solve this trig identity? (cos(4theta)-cos(10theta))/(sin(4theta)+sin(10theta))

cos-4theta

#1

Anyone can establish and solve this trig identity? (cos(4theta)-cos(10theta))/(sin(4theta)+sin(10theta))=tan(3theta)

Answer:

Numerator
[ cos(4t) - cos(10t) ] =
= -2 * sin [ (4t + 10t) / 2 ] * sin [ (4t - 10t) / 2 ]
= -2 * sin (7t) * sin (-3t)
= 2 * sin (7t) * sin (3t)

Denominator
[ sin(4t) + sin(10t) ] =
= 2 * sin [ (4t + 10t) / 2] * cos [ (4t - 10t) / 2 ]
= 2 * sin (7t) * cos (-3t)
= 2 * sin (7t) * cos (3t)

Numerator / Denominator =
= [ 2 * sin (7t) * sin (3t) ] / [ 2 * sin (7t) * cos (3t) ]
= [ sin (3t) ] / [ cos (3t) ]
= tan(3t)