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

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Answer 1 · 2017-11-08T11:29:57

See below.

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.