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in Trigonometry by (47.4k points)
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Prove that \(\frac{sin\theta-cos\theta+1}{sin\theta+cos\theta-1}\) = \(\frac{1}{sec\theta\,-\,tan\theta}\) using the identity sec2 θ = 1 + tanθ.

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Since we will apply the identity involving sec θ and tan θ, let us first convert the LHS (of the identity we need to prove) in terms of sec θ and tan θ by dividing numerator and denominator by cos θ.

LHS

Which is the RHS of the identity, we are required to prove.

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