Question

tan detha + sec detha -1/ tan detha - sec detha +1= 1+ sin detha/cos detha​

Answer 1

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