Question

tan thita + sec thita - 1 / tan thita - sec thita + 1 = 1 + sin thita / cos thita

Answer 1

tan theta + sec theta -1/tan theta -sec theta +1
(tan theta + sec theta) - (sec sq theta - tan sq theta)/tan theta - sec theta +1
(tan theta + sec theta)- [(sec theta + tan theta)(sec theta- tan theta)]/tan theta - sec theta +1
tan theta + sec theta (1 - sec theta. + tan theta)/tan theta - sec theta + 1)
upper lower cancel
now tan theta + sec theta
sin theta /cos theta+1/cos theta
1 + sin theta/ cos theta RHS proved


hope it helps..