Question

The general solution of
sin x - 3 sin 2x + sin 3x = cos x - 3cos 2x + cos 3x is​

Answer 1

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Answer 2

Answer:

= nπ/2 +π/8 , n∈Z

Step-by-step explanation:

We have, (sin x + sin 3x) – 3 sin 2x = (cos x + cos 3x) – 3 cos 2x

=> 2 sin 2x cos x – 3 sin 2x = 2 cos 2x.cos x – 3 cos 2x

=> sin 2x(2 cos x – 3) = cos 2x(2 cos x – 3)

=> sin 2x = cos 2x (As cos x ≠ 3/2)

=> tan 2x = 1 => tan 2x = tan π/4

=> 2x = nπ + π/4 , n∈Z x = nπ/2 +π/8 , n∈Z