Prove that `sec theta+tan theta=(cos theta)/(1-sin theta)`

1.	Prove that `sec theta+tan theta=(cos theta)/(1-sin theta)`
Answer» Proof: `LHS=sec theta+tan theta` `=1/(cos theta)+(sin theta)/(cos theta)………[sec theta=1/(cos theta), tan theta=(sin theta)/(cos theta)]` `=(1+sin theta)/(cos theta)` `=((1+sin theta))/(cos theta)xx((1-sin theta))/((1- sin theta))`……….. (Multiplying the numerator and denominator by `1-sin theta`) `=((1)^(2)-sin^(2)theta)/(cos theta(1-sin theta))............[(a+b)(a-b)=a^(2)-b^(2)]` `=(cos^(2) theta)/(cos theta(1-sin theta)){:[(sin^(2)theta+cos^(2)theta=1),( :.cos^(2)theta=1-sin^(2)theta)]:}` `=(cos theta)/(1-sin theta)=RHS` `:. sec theta+tan theta=(cos theta)/(1-sin theta)`

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