verify that (sin3x)/sinx=3-4sin^2x?

Answer 1

sin3x = sin (x+ 2x)
= sinx.cos2x + cosx.sin2x
= sinx (2cos^2x -1) + cosx (2sinx.cosx)
= 2sinx.cos^2x - sinx + 2sinx.cos^2x
= sinx (2cos^2x - 1 + 2cos^2x)
= sinx (4cos^2x - 1)

But, cos^2x = 1 - sin^2x
so then,

sin3x = sinx [ 4 - 4sin^2x - 1]
= sinx (3 - 4sin^2x)

Therefore,

sin3x/sinx = sinx(3 - 4sin^2x)/sinx
= 3 - 4sin^2x --- answer.

Answer 2

some idiots think of i'm purely "human", yet a good number of the time i've got faith like an animal (lioness and a monkey). there is not any verification that "I" am a human, different than via the "scientists"? nicely I even have information for them. some won't be able to see or pay attention me. Floating religious power trapped interior the "human physique cage" till the cage rusts away my spirits are trapped. interior the recommend time, i will proceed to swing on the swing, leap on my mattress, climb trees, run up sand dunes with bare ft and bypass by using puddles of water. Oh yeah, considering i'm nocturnal i would be a bat, opposum or extra desirable a clever nighttime owl.

Answer 3

sin(3x) / sinx = sin(2x+x) /sinx

= (sin2xcosx + cos2x sinx ) / sinx

= (2sinxcosx cosx + cos2x sinx) / sinx

= 2 (cos x) ^2 + cos2x

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

= 3 (cos x)^2 - (sin x) ^2

= 3( 1 - (sin x) ^2) - (sin x) ^2

= 3 - 4 (sin x) ^2

Answer 4

Sin? If sin that really that complicated - I promise I won't commit them anymore!

Answer 5

sin(3x)=sin(2x+x)=
sin(2x)cos(x)+cos(2x)sin(x)

sin(2x)=2sin(x)cos(x)
cos(2x)=cos^2(x)-sin^2(x)
so substitute

2sin(x)cos^2(x)+sin(x)cos^2(x)-sin^3(x)
divide this by sin(x)

2cos^2(x)+cos^2(x)-sin^2(x)=
3cos^2(x)-sin^2(x)
add 3sin^2(x) but then subtract them as well to get:
3cos^2(x)+3sin^2(x)-3sin^2(x)-sin^2(x)=
3(cos^2(x)+sin^2(x))-4sin^2(x)=

3-4sin^2(x)

note: cos^2(x)+sin^2(x)=1

Answer 6

if you know that, then you're really a nerd.