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Question
If cot θ = `3/4` , show that `sqrt("sec θ - cosecθ"/"secθ + cosecθ" ) = 1/ sqrt(7)`
Solution
LHS = `sqrt(" sec θ - cosec θ "/"secθ + cosecθ")`
=`sqrt(((1/costheta-1/sintheta))/((1/costheta+1/(sin theta)))`
=`sqrt((((sintheta-costheta)/(sintheta costheta)))/(((sintheta + costheta)/(sintheta costhet)))`
=`sqrt((((sintheta-costheta)/(sintheta)))/(((sintheta + costheta)/(sintheta)))`
=`sqrt((((sintheta) /(sintheta)-(costheta)/sintheta))/(((sintheta)/(sintheta)+(costheta)/(sintheta)))`
=`sqrt((1-costheta)/(1+costheta))`
=`sqrt(((1-3/4))/((1+3/4)))`
=`sqrt(((1/4))/((7/4)))`
=`sqrt(1/7)`
=`1/sqrt(7)`
= RHS
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