Question

if tan theta plus cot theta = 2 find sin theta​

Answer 1

$\tan( \alpha ) + \cot( \alpha ) = 2 \\ \frac{ \sin( \alpha ) }{ \cos( \alpha ) } + \frac{ \cos( \alpha ) }{ \sin( \alpha ) } = 2 \\ { {\sin( \alpha ) } }^{2} + {cos \alpha }^{2} = 2sin \alpha \cos( \alpha ) \\ \sin( \alpha ) ^{2} - 2 \sin( \alpha ) \cos( \alpha ) + cos \alpha {}^{2} = 0 \\ (sin \alpha - \cos( \alpha ) ) {}^{2} = 0 \\ \sin( \alpha ) = \cos( \alpha )$

Answer 2

$heya \\ \\ \\ we \: know \: that \: \: 1 + \tan {}^{2} ( \alpha ) = \sec {}^{2} ( \alpha ) \\ \\ \cot( \alpha ) = \cos( \alpha ) \div \sin( \alpha ) \\ \\ \\ \\ = > \\ \\ (1 + \tan {}^{2} ( \alpha ) ) \\ - - - - - - \: \: \: = {2} \\ \tan( \alpha ) \\ \\ \\ \\ = > \\ \\\sec {}^{2}( \alpha ) \times \cot( \alpha ) = 2 \\ \\ \\ \csc(2 \alpha ) = 1 \\ \\ = > \\ \\ \\ \alpha = 45 \\ \\ \\ so \: \: \: \: \sin( \alpha ) = 1 \div \sqrt{2}$