Verify the identity tan^2 theta/sec theta=sin theta tan theta Can someone explain to me how to do this please?

See below.

Explanation:

Using identities:

#secx=1/cosx# and , #tanx=sinx/cosx#

So we can write:

#((sin^2theta)/(cos^2theta))/(1/costheta)#

Multiplying by #costheta#

#(sin^2thetacostheta)/(cos^2theta)#

Cancelling:

#(sin^2thetacancel(costheta))/(costheta)#

We can express this as:

#(sinthetasintheta)/costheta#

Since #sintheta/costheta=tantheta#

We have:

#sinthetatantheta#

#LHS -= RHS#

Hope this helps you.