Question

Sin theeta 1\3 then value of 1+cotsquare theeta

Answer 1

$\huge \underline \bold \color{orchid} \mathfrak{Answer}$

For the sake of simplicity, we have taken theta as alpha.

$\sin( \alpha ) = \frac{1}{3} --- given$

$\sin {}^{2} ( \alpha ) = ( \frac{1}{3} ) {}^{2}$

$\sin {}^{2} ( \alpha ) = \frac{1}{9}$

$1 + \cot {}^{2} ( \alpha ) = cosec {}^{2} ( \alpha )$

$as \: \cosec {}^{2} ( \alpha ) - \cot {}^{2} ( { \alpha } ) = 1$

$\cosec {}^{2} ( \alpha ) = \frac{1}{ \sin {}^{2} ( \alpha ) }$

$\cosec {}^{2} \alpha = \frac{1}{ \frac{1}{9} }$

$\cosec {}^{2} ( \alpha ) = 9$

Therefore,

$1 + \cot {}^{2} ( \alpha ) = 9$