Question

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

Answer 1

Answer:

See the verification below.

Step-by-step 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