(cotx/1+sinx) + (cosx/1-sinx) = tanx+secxcscx may i please get help with verifying this equation?

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pramodpandey | College Teacher | (Level 3) Valedictorian

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`cotx/(1+sinx)+cosx/(1-sinx)= (cosx/sinx)(1/(1+sinx))+cosx/(1-sinx)` ,  here we have,`{cotx=cosx/sinx ,cotx/(1+sinx)=cotx*(1/(1+sinx))}`

`cosx/(sinx(1+sinx))+cosx/(1-sinx)=cosx(1/(sinx(1+sinx))+1/(1-sinx))`

`=cosx((1-sinx+sinx(1+sinx))/(sinx(1+sinx)(1-sinx)))=`

`cosx((1-sinx+sinx+sin^2x)/(sinx(1-sin^2x)))=cosx((1+sin^2x)/(sinx cos^2x))`

`=cosx/(sinx cos^2x)+(cosx sin^2x)/(sinx cos^2x)=`

`=1/(sinx cosx)+sinx/tanx=cscxsecx+tanx`

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