Question

Plzz solve the above question ☝️

Answer 1

Solution:-

$\rm \dfrac{ \cos\theta}{1 - \tan\theta } + \dfrac{ \sin \theta}{1 - \cot\theta }$

$\dfrac{ \cos\theta }{1 - \dfrac{ \sin \theta}{ \cos \theta } } + \dfrac{ \sin\theta }{1 - \dfrac{ \cos \theta }{ \sin\theta} }$

$\dfrac{ \cos \theta }{ \dfrac{ \cos\theta - \sin\theta }{ \cos\theta } } + \dfrac{ \sin \theta }{ \dfrac{ \sin\theta - \cos \theta }{ \sin \theta} }$

$\dfrac{ \cos {}^{2} \theta }{ \cos\theta - \sin \theta } + \dfrac{ \sin {}^{2} \theta }{ \sin\theta - \cos \theta }$

$\dfrac{ \cos {}^{2} \theta }{ \cos \theta - \sin\theta } - \dfrac{ \sin {}^{2} \theta }{ \cos\theta - \sin \theta }$

$\dfrac{ \cos {}^{2} \theta - \sin {}^{2} \theta}{ \cos\theta - \sin\theta }$

$\dfrac{(\cos\theta - \sin\theta )(\cos\theta + \sin\theta )}{\cos\theta - \sin\theta }$

Answer

$\cos\theta + \sin\theta$