Question

Please help! Prove: cos θ - cos θ•sin2 θ = cos3 θ. You must show all work.

Answer 1

which are exponents and which are not? ARe there any exponents ?

Answer 2

like sin^2x or sin(2x) ?

Answer 3

im not sure :/

Answer 4

\(\Large\color{black}{ \bf cos θ - cos θ~sin^2 θ = cos^3 θ }\)

like this ?

Answer 5

there is supposed to be a multiplication in between cos0 and sin^20

Answer 6

i think

Answer 7

When there is no space that's what it means (just like "ab" mean a times b )

Anyway, ....

\(\Large\color{black}{ \bf cos θ - cosθ~sin^2 θ= cos^3 θ }\)


factor out of cos θ on the left


\(\Large\color{black}{ \bf cos θ(1 - ~sin^2 θ) = cos^3 θ }\)

Answer 8

\(\Large\color{black}{ \bf cos θ(1 - ~sin^2 θ) = cos^3 θ }\)


Divide both sides by cos θ,


\(\Large\color{black}{ \bf 1 - ~sin^2 θ = cos^2 θ }\)


add sin^2 θ to both sides


\(\Large\color{black}{ \bf 1= cos^2 θ+ ~sin^2 θ }\)

Answer 9

thankyou so much, would that be my final answer or do i still need to add?

Answer 10

No, that is considered to be authentic, although, there is a proof to it as well.

Answer 11

thankyou!!