Question

Prove: sin θ - sin θ•cos2 θ = sin3 θ. You must show all work.

Answer 1

@welshfella

Answer 2

Is cos2theta ''cos to the power 2 theta'' or ''cos of 2theta''?

Answer 3

i feel something is missing in it.

Answer 4

thats the exact question so thats all they gave me

Answer 5

we have to apply this identity, at the left side:
\[\large {\left( {\cos \theta } \right)^2} = 1 - {\left( {\sin \theta } \right)^2}\]

Answer 6

so, you should get this:
\[\large \sin \theta - \sin \theta {\left( {\cos \theta } \right)^2} = \sin \theta - \sin \theta \left[ {1 - {{\left( {\sin \theta } \right)}^2}} \right] = ...?\]

Answer 7

\[\sin(\theta)-\sin(\theta)(\cos^2(\theta)=\sin(\theta)[1-\cos^2(\theta)]=\sin(\theta)(\sin^2(\theta)=\sin^3(\theta)\]

Answer 8

sin^3(0)

Answer 9

that's right!

Answer 10

it should be sin^3(theta) else the equation become 0=sin^3(theta)

Answer 11

so that the answer??

Answer 12

obliously sin^3(theta)

Answer 13

yes! Since we have showed, that the left side is equal to the right side

Answer 14

thankyou guys

Answer 15

thank you!

Answer 16

you are welcome.!