Prove `:(sec theta-cos theta)(cot theta+tan theta)=tan .sec theta`

Explanation

Proof:
`LHS=(sec theta-cos theta)(cot theta+tan theta)`
`=(1/(cos theta)-cos theta)((cos theta)/(sin theta)+(sin theta)/(cos theta))`
…..`[sec theta=1/(cos theta),cot theta=(cos theta)/(sin theta)` and `tan theta=(sin theta)/(cos theta)]`
`=((1-cos^(2)theta)/(cos theta))((cos^(2)theta+sin^(2)theta)/(sin theta.cos theta))`
`=(sin^(2)theta)/(cos theta)xx1/(sin theta.cos theta).........{:[( :' sin^(2) theta+cos^(2)=1),( :.sin^(2)theta=1-cos^(2) theta)]:}`
`=(sin theta)/(cos theta)xx1/(cos theta)`
`=tan theta xx sec theta`...... `[ :' (sin theta)/(cos theta)=tan theta, 1/(cos theta)=sec theta]`
`=RHS`
`:.(sec theta-cos theta)(cot theta+tan theta)=tan theta.sec theta`.