Prove that: tan theta - 1 …

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Sia ? 6 years, 6 months ago
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} {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}
= {tex}tan\theta+sec\theta{/tex}
= R.H.S.
Hence Proved.
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