Question

please anwser this question ​

Answer 1

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$\frac{sin \theta - cos \theta + 1}{sin \theta + cos \theta - 1} \\ = \frac{ \frac{sin \theta - cos \theta + 1}{cos \theta } }{ \frac{sin \theta + cos \theta - 1}{cos \theta } } \\ = \frac{tan \theta+ sec \theta - 1 }{tan \theta - sec \alpha + 1} \\ = \frac{tan \theta + sec \theta- 1}{ - (sec \theta - tan \theta) + ( {sec}^{2} \theta - {tan}^{2} \theta )} \\ = \frac{tan \theta + sec \: - 1}{(sec \theta - tan \theta )( - 1 + sec \theta + tan \theta )} \\ = \frac{1}{sec \theta - tan \theta}$

Answer 2

Refer the attachment for complete answer ✔️

Trigonometric identities :

sin² a + cos² a = 1

1+tan² a = sec² a

cosec² a = 1 + cot² a