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Question
`(sectheta- tan theta)/(sec theta + tan theta) = ( cos ^2 theta)/( (1+ sin theta)^2)`
Solution
LHS= `(sectheta- tan theta)/(sec theta + tan theta)`
= `(1/cos theta-sin theta/cos theta)/(1/cos theta+ sin theta/cos theta)`
=`((1-sin theta)/cos theta)/((1+ sin theta)/cos theta)`
=`(1-sin theta)/(1+ sin theta)`
=`((1-sin theta) (1+ sin theta))/( (1+ sin theta )(1+ sin theta)) {"Dividing the numerator and
denominator by"(1 + cos theta)}`
=`((1-sin^2 theta))/((1+ sin theta)^2)`
=`cos^2 theta/(1+ sin theta)^2`
= RHS
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