Question

the general solution of sinx- 3 sin2x + sin3x = cosx - 3cos2x + cos3x​

Answer 1

YES

Step-by-step explanation:

2sin2xcosx−3sin2x=2cos2xcosx−3cos2x

(2cosx−3)sin2x=(2cosx−3)cos2

cos2x=sin2

tan2x=1

x=2nΠ+8Π

Answer 2

Answer:

nπ/2+π/8

Step-by-step explanation:

We have, (sinx+sin3x)−3sin2x=(cosx+cos3x)−3cos2x

⇒2sin2xcosx−3sin 2x=2cos 2x cos x−3 cos 2x

⇒sin2x(2cosx−3)=cos2x(2cosx−3)

⇒sin2x=cos2x(Ascosx=3/2)

⇒tan 2x=1⇒tan 2x=tan π/4

⇒2x=nπ+π/4,n∈Z

x= nπ/2+π/8,n∈Z

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