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

The correct option is C ${\sin }^3\theta +{\cos }^3\theta$

$\sin \theta +\cos \theta -{\sin }^2\theta \cos \theta -\sin \theta {\cos }^2\theta$
$=\cos \theta (1-{\sin }^2\theta )+\sin \theta (1-{\cos }^2\theta )={\cos }^3\theta +{\sin }^3\theta$.