Question 117947
When you prove identities, you only manipulate <b>one side</b>. So I'm going to change the left side into the right side



sin^2x - sin^4x = (cos^2x)(sin^2x).....Start with the given equation



sin^2x - (sin^2x)(sin^2x)  = (cos^2x)(sin^2x).....Rewrite sin^4x as (sin^2x)(sin^2x)



sin^2x(1 - sin^2x)  = (cos^2x)(sin^2x).....Factor out sin^2x



sin^2x(cos^2x)  = (cos^2x)(sin^2x).....Replace 1-sin^2x with cos^2x




(cos^2x)(sin^2x)  = (cos^2x)(sin^2x).....Rearrange the left side




So this verifies the identity