Question

$(\sin \theta +\cos \theta )(1-\sin \theta \cos \theta )$ can be written as :

• A. $\sin \theta +\cos \theta$
• B. ${\sin }^3\theta -{\cos }^3\theta$
• C. ${\sin }^3\theta +{\cos }^3\theta$
• D. $\sin \theta -\cos \theta$

Answer 1

Answer: (C)

${\sin }^3\theta +{\cos }^3\theta$

$(\sin \theta +\cos \theta )(1-\sin \theta \cos \theta )$ can be written as

$(\sin \theta +\cos \theta )({\sin }^2\theta +{\cos }^2\theta -\sin \theta .\cos \theta )$
$={\sin }^3\theta +{\cos }^3\theta$