Prove that tanq+Secq-1÷tanq-secq+1=cosq÷1-sinq

Here am going to explain the steps Prove that tanq+Secq-1÷tanq-secq+1=cosq÷1-sinq

LHS => tanq+Secq-1/tanq-secq+1

=> (sinQ/cosQ+1/cosQ-1)/(sinQ/cosQ-1/cosQ+1) (divide nominator and denominate by cosQ)

=> (sinQ+1-cosQ)/(sinQ-1+cosQ) (Multipy nominator and denominate by (1-sinQ))

=> (1-sinQ)(sinQ+1-cosQ)/(1-sinQ)(sinQ-1+cosQ)

=> (sinQ+1-cosQ-sinQ2-sinQ+sinQ*cosQ)/(1-sinQ)(sinQ-1+cosQ)

=> (1-cosQ-sinQ2+sinQ*cosQ)/(1-sinQ)(sinQ-1+cosQ)
=> (1-sinQ2-cosQ+sinQ*cosQ)/(1-sinQ)(sinQ-1+cosQ)

=> (cosQ2-cosQ+sinQ*cosQ)/(1-sinQ)(sinQ-1+cosQ)
=> cosQ(cosQ-1+sinQ)/(1-sinQ)(sinQ-1+cosQ)

=> cosQ(cosQ-1+sinQ)/(1-sinQ)(cosQ-1+sinQ)
=> cosQ/(1-sinQ) = RHS

Hence proved

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