Answer:
See the verification below.
Step-by-step explanation:
Starting expression: [tex]sin^3(x)+sin(x)\,cos^2(x)=sin(x)[/tex]
Extract from the expression on the left of the equal sign the common factor "sin(x)":
[tex]sin^3(x)+sin(x)\,cos^2(x)=sin(x)\\sin(x)[sin^2(x)+cos^2(x)]=sin(x)[/tex]
Now use the Pythagorean trigonometric identity: [tex]sin^2(x)+cos^2(x)=1[/tex] to replace the expression in between square brackets with "1":
[tex]sin(x)[sin^2(x)+cos^2(x)]=sin(x)\\sin(x) \,[1]=sin(x)\\sin(x)=sin(x)[/tex]
Therefore we have verified the identity
