## Question

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

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

## Answers

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.

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