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Question
`sqrt((1+cos theta)/(1-cos theta)) + sqrt((1-cos theta )/(1+ cos theta )) = 2 cosec theta`
Solution
LHS=`sqrt((1+cos theta)/(1-cos theta)) + sqrt((1-cos theta )/(1+ cos theta ))`
=`sqrt(((1+cos theta)^2)/((1-cos theta)(1+ cos theta))) + sqrt (((1-cos theta)^2)/((1+ cos theta) (1- cos theta))`
=`sqrt(((1+cos theta)^2)/((1-cos^2 theta))) + sqrt(((1-cos theta )^2)/((1-cos^2 theta))`
=` sqrt(((1+ cos theta)^2)/(sin^2 theta))+sqrt(((1-cos theta
)^2)/sin^2 theta)`
=`((1+cos theta))/(sin theta) + ((1-cos theta))/(sin theta)`
=`(1+ cos theta +1-cos theta)/sin theta`
=`2/sin theta`
= 2cos ecθ
= RHS
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