Question

Last trig question!! Please explain how to do this!! Thank youuu !!!!!!

Answer 1

yes

Explanation:

Answer 2

See the verification below.

Explanation:

Starting expression:
`sin^3(x)+sin(x)\,cos^2(x)=sin(x)`

Extract from the expression on the left of the equal sign the common factor "sin(x)":

`sin^3(x)+sin(x)\,cos^2(x)=sin(x)\\sin(x)[sin^2(x)+cos^2(x)]=sin(x)`

Now use the Pythagorean trigonometric identity:
`sin^2(x)+cos^2(x)=1` to replace the expression in between square brackets with "1":

`sin(x)[sin^2(x)+cos^2(x)]=sin(x)\\sin(x) \,[1]=sin(x)\\sin(x)=sin(x)`

Therefore we have verified the identity