Verify the identity Sin^3x + (Sinx) cos^2x = sinx?

Question

AHHH!  Trig is so confusing!

panic mode · Accepted Answer

divide everything by sin(x) and you get
sin^2x+cos^2x=1 which is basic identity

Rameshwar · Answer

L.H.S. = sin^3x    + sinx    cos^2x  
                  = sinx (  sin^2x + cos^2x )
                  = sinx (1)= sinx =R.H.S.

William B · Answer

sin^3x +sinxcos^2x =
sinx(sin^2x +cos^2x)=
sinx (1)=
sinx

Brach Z · Answer

Show that sinÂ³x + sin x cosÂ²x = sin x.

Recall that sinÂ²x + cosÂ²x = 1.

Therefore,

sinÂ³x + sin x cosÂ²x

= sinÂ³x + sin x (1 - sinÂ²x)

= sinÂ³x + sin x - sinÂ³x

= sin x.

Or alternatively,

sinÂ³x + sin x cosÂ²x

= (sin x) (sinÂ²x + cosÂ²x)

= (sin x) (1)

= sin x.

MechEng2030 · Answer

factoring out a sin(x) on the l.h.s:

sin(x)[sinÂ²(x) + cosÂ²(x)] = sin(x)*1 = sin(x)

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