Question

Hello, I would appreciate if someone could help me with this trig problem.. Deals with identities

sin θ - sin θ•cos^2 θ = sin^3 θ

Answer 1

\[\huge\rm cos^2 \theta = ??\]

Answer 2

cos^2 = 1-sin^2 right....

Answer 3

yep! :-)
so replace cos^2 by 1- sin^2 :-)

Answer 4

okay, after that do i just factor a sinx?

Answer 5

\[\huge\rm sin \theta - \sin \theta \times \color{red}{ 1 - \sin^2 \theta }\]
multiply 1 - sin^2 by sin

Answer 6

\[\huge\rm sin \theta - \sin \theta \times \color{red}{( 1 - \sin^2 \theta )}\]let's put parentheses

Answer 7

--> sinx(sinx-sin^3x)=sin^3

Answer 8

hmm where is negative sign ??
who kidnapped NEGATIVE sign !!

Answer 9

oops sorry bout that..

Answer 10

what would i do next?

Answer 11

\[\huge\rm sin \theta \color{blue}{-}\color{red}{ [}\sin \theta \times \color{red}{( 1 - \sin^2 \theta )]}\] so sin(1-sin^2) = sin - sin^3
\[\huge\rm sin \theta \color{blue}{-}\color{red}{ [} \color{red}{( sin \theta - sin^3 \theta )]}\]
distribute bracket by negative sign

Answer 12

why did you delete that ?? :(

Answer 13

Because i made a mistake... lol

Answer 14

add sin^3x to make the right side 2sin^3x

Answer 15

you have to verify
both sides should be equal
so don't need to touch right side

Answer 16

verify identities **

Answer 17

oh okay

Answer 18

let me what u get after distributing bracket by negative sign ?

Answer 19

sinx-sinx+sin^3x=sin^3x

Answer 20

sinx-sinx= 0

Answer 21

yes right :-)

Answer 22

leaving

sin^3x=sin^3x

Answer 23

gO_Od to go! :-)
nice job!

Answer 24

Thank you so much!

Answer 25

my pleasure :-)
btw \(\huge\color{Green}{{\rm welcome}\rm~to~open~study!!!!}\)\(\Huge \color{gold}{\star^{ \star^{\star:)}}}\Huge \color{green}{\star^{ \star^{\star:)}}}\)
\(\Huge \color{blue}{\star^{ \star^{\star:)}}}\Huge \color{red}{\star^{ \star^{\star:)}}}\)\(\rm\color{green}{o^\wedge\_^\wedge o}\)

Answer 26

for what it's worth , you could do
sin θ - sin θ•cos^2 θ = sin^3 θ

factor out sin on the left side to get
sin θ ( 1- cos^2 θ ) = sin^3 θ

use the identity to replace 1- cos^2 with sin^2
sin θ sin^2 θ = sin^3 θ

simplify the left side
sin^3 θ = sin^3 θ

which shows the identity