How do I prove this equation is an identity? sin^3+sin(x)cos^2(x)/cos(x)=tan(x)

1 Answer
Mar 18, 2018

Verified below

Explanation:

sin3x+sin(x)cos2(x)cos(x)=tan(x)

GCF:
sinx(sin2x+cos2x)cos(x)=tan(x)

Apply the pythagorean identity:
sin2x+cos2x=1

Therefore:
sinx(1)cos(x)=tan(x)
sinxcosx=tan(x)

Apply the quotient identity:
sinxcosx=tanx

Therefore:
tanx=tanx