Question

( sin3x + sinx )sinx + (cos3x - cosx)cosx=0 prove it

Answer 1

Answer :

Now,

(sin3x + sinx) sinx + (cos3x - cosx) cosx

= sin3x sinx + sin²x + cos3x cosx - cos²x

= (cos3x cosx + sin3x sinx) - (cos²x - sin²x)

= cos(3x - x) - cos2x

= cos2x - cos2x

= 0

Hence, proved.

Trigonometric Identities :

cos(A - B) = cosA cosB + sinA sinB

cos2A = cos²A - sin²A

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Answer 2

Answer:

proved

Step-by-step explanation:

(sin3x + sinx) sinx + (cos3x - cosx) cosx=0

L.H.S.= sin3xsinx + sin^2x + cos3xcosx - cos^2x

= (cos3xcosx + sin3xsinx) - ( cos^2x - sin^2x)

=cos(3x-x) - cos2x

= cos2x - cos2x

=0

= R.H.S.