please solve it's aurgent
Answers
We have to prove LHS = RHS
LHS = ( tan\theta+sec\theta-1 ) / ( tan\theta-sec\theta+1 )(tanθ+secθ−1)/(tanθ−secθ+1)
RHS = (sin\theta+1) / cos\theta(sinθ+1)/cosθ
Lets Start from LHS
LHS = ( tan\theta+sec\theta-1 ) / (tan\theta-sec\theta+1 )(tanθ+secθ−1)/(tanθ−secθ+1)
= ( tan\theta+sec\theta-(sec^{2}\theta-tan^2\theta )) / ( tan\theta-sec\theta+1 )(tanθ+secθ−(sec
2
θ−tan
2
θ))/(tanθ−secθ+1)
= (tan\theta+sec\theta-[(sec\theta+tan\theta)(sec\theta-tan\theta)])/(tan\theta-sec\theta+1 )(tanθ+secθ−[(secθ+tanθ)(secθ−tanθ)])/(tanθ−secθ+1)
= (tan\theta+sec\theta[tan\theta-sec\theta+1]) / (tan\theta-sec\theta+1 )(tanθ+secθ[tanθ−secθ+1])/(tanθ−secθ+1)
= tan\theta+sec\thetatanθ+secθ
= [sin\theta/cos\theta] + [1/cos\theta][sinθ/cosθ]+[1/cosθ]
= [(sin\theta+1) /cos\theta][(sinθ+1)/cosθ] = RHS
Hence Proved,
LHS=RHS