How can you prove this? (Cscx+1/cscx-1)-(secx-tanx/secx+tanx)=4tanxsecx

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Answer 1 · 2018-04-06T05:55:40

Please refer to a Proof in Explanation.

#(cscx+1)/(cscx-1)-(secx-tanx)/(secx+tanx)#,

#={(1/sinx+1)-:(1/sinx-1)}-{(1/cosx-sinx/cosx)-:(1/cosx+sinx/cosx)}#,

#={(1+sinx)/sinx-:(1-sinx)/sinx}-{(1-sinx)/cosx-:(1+sinx)/cosx}#,

#=(1+sinx)/(1-sinx)-(1-sinx)/(1+sinx)#,

#={(1+sinx)^2-(1-sinx)^2}/{(1-sinx)(1+sinx)}#,

#={(1+2sinx+sin^2x)-(1-2sinx+sin^2x)}/(1-sin^2x)#,

#=(4sinx)/cos^2x#,

#=4*sinx/cosx*1/cosx#,

#=4tanxsecx#, as desired!