Question

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

Answer 1

Verified below

Explanation:

`(sin^3x+sin(x)cos^2(x))/cos(x)=tan(x)`

GCF:
`(sinx(sin^2x+cos^2x))/cos(x)=tan(x)`

Apply the pythagorean identity:
`sin^2x+cos^2x=1`

Therefore:
`(sinx(1))/cos(x)=tan(x)`
`sinx/cosx=tan(x)`

Apply the quotient identity:
`sinx/cosx= tanx`

Therefore:
`tanx=tanx`