( sin theta + cos theta …

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Sia ? 6 years, 6 months ago
L.H.S. {tex}= (\sin \theta + \cos \theta )(\tan \theta + \cot \theta ){/tex}
{tex}= (\sin \theta + \cos \theta )\left( {\frac{{\sin \theta }}{{\cos \theta }} + \frac{{\cos \theta }}{{\sin \theta }}} \right){/tex}
{tex}= (\sin \theta + \cos \theta )\left( {\frac{{{{\sin }^2}\theta + {{\cos }^2}\theta }}{{\sin \theta \cos \theta }}} \right){/tex}
{tex} = (\sin \theta + \cos \theta )\left( {\frac{1}{{\sin \theta \cos \theta }}} \right){/tex}
{tex} = \frac{{\sin \theta + \cos \theta }}{{\sin \theta \cos \theta }}{/tex}
{tex} = \frac{{\sin \theta }}{{\sin \theta \cos \theta }} + \frac{{\cos \theta }}{{\sin \theta \cos \theta }}{/tex}
{tex}= \frac{1}{{\cos \theta }} + \frac{1}{{\sin \theta }}{/tex}
{tex}= \sec \theta + \cos ec\theta {/tex}
= R.H.S.
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