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(sintheta)/(1+costheta) + (1+costheta)/(...

`(sintheta)/(1+costheta) + (1+costheta)/(sintheta) = 2 cosec theta`

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LHS= `(sintheta)/(1+costheta) + (1+costheta)/(sintheta) = (sin^(2)theta+ (1+costheta)^(2))/(sintheta(1+costheta))`
`=(sin^(2)theta + 1 + cos^(2)theta+ 2 costheta)/(sintheta(1+costheta))` `[therefore (a+b)^(2)=a^(2)+b^(2)+2ab)]`
`=(1+1+2costheta)/(sintheta(1+costheta))` `[therefore sin^(2)theta + cos^(2)theta=1]`
`=(2(1+costheta))/(sintheta(1+costheta))= 2/(sintheta)`
`=2cosectheta = RHS` `[therefore cosectheta=1/sintheta]`
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