Tan s / 1 + cos s + sin s / 1 - cos s = cot s + sec s csc s

Question

this is a proving identities using fundamental identites.

please answer this. I really really need it.

Many thanks to those who can answer. :)

Answer 1

Left handside identity = Tans/(1+Coss)+Sins/(1-Coss)

= Tans(1-Coss)/(1+Coss)(1-Coss)+Sins(1+Coss)/(1-Coss)(1+Coss)

= Tans(1-Coss)/(1-Cos^2s)+Sins(1+Coss)/(1-Cos^2s)

We know that Sin^2s = 1-Cos^2s,Tans = Sins/Coss

= (Sins/Coss)(1-Coss)/Sin^2s+Sins(1+Coss)/Sin^2s

= [ (Sins/Coss)(1-Coss)+Sins(1+Coss)]/Sin^2s

= [(1-Coss)/Coss+(1+Coss)]/Sins

= [(1-Coss)/Coss+(1+Coss)(Coss/Coss)]/Sins

= [((1-Coss)+(1+Coss)Coss)/Coss]/Sins

= [1-Coss+Coss+Cos^2s]/SinsCoss

= (1+Cos^2s)/SinsCoss

= 1/SinsCoss+Cos^2s/SinsCoss

= CscsSecs+Cots

= Right hand side identity.