Prove that:tan theta - 1 + sec theta / tan theta + 1-sec theta = 1 / sec theta - tan theta

Prove that:tan theta - 1 + sec theta / tan theta + 1-sec theta = 1 / s

1.	Prove that:tan theta - 1 + sec theta / tan theta + 1-sec theta = 1 / sec theta - tan theta
Answer» L.H.S={tex}\\frac { \\tan \\theta + \\sec \\theta - 1 } { \\tan \\theta - \\sec \\theta + 1 }{/tex}{tex}= \\frac { ( \\tan \\theta + \\sec \\theta ) - \\left( \\sec ^ { 2 } \\theta - \\tan ^ { 2 } \\theta \\right) } { \\tan \\theta - \\sec \\theta + 1 }{/tex}\xa0{tex}[\\because sec^2\\theta-tan^2\\theta=1]{/tex}{tex}= \\frac { ( \\tan \\theta + \\sec \\theta ) - ( \\sec \\theta - \\tan \\theta ) ( \\sec \\theta + \\tan \\theta ) } { \\tan \\theta - \\sec \\theta + 1 }{/tex}{tex}= \\frac { ( \\tan \\theta + \\sec \\theta ) [ 1 - \\sec \\theta + \\tan \\theta ] } { \\tan \\theta - \\sec \\theta + 1 }{/tex}=\xa0{tex}tan\\theta+sec\\theta{/tex}= R.H.S.Hence Proved.