Question

Prove :
$\frac{{sin}^3\theta +{cos}^3\theta }{sin\theta +cos\theta }+sin\theta .cos\theta =1?$

Answer 1

L.H.S$=\frac{{\sin }^3\theta +{\cos }^3\theta }{\sin \theta +\cos \theta }+\sin \theta \cos \theta$

$=\frac{(\sin \theta +\cos \theta )({\sin }^2\theta +{\cos }^2\theta -\sin \theta \cos \theta )}{\sin \theta +\cos \theta }+\sin \theta \cos \theta$

$=1-\sin \theta \cos \theta +\sin \theta \cos \theta$

$=1=$R.H.S

Hence proved.