Jambmaths question:
Differentiate ${{(\cos \theta -\sin \theta )}^{2}}$ with respect to θ
Option A:
$-2\sin 2\theta$
Option B:
$-2\cos 2\theta$
Option C:
$1-2\cos 2\theta$
Option D:
$1-2\sin 2\theta$
Jamb Maths Solution:
$\begin{align} & y={{(\cos \theta -\sin \theta )}^{2}}=(\cos \theta -\sin \theta )(\cos \theta -\sin \theta ) \\ & y={{\cos }^{2}}\theta +{{\sin }^{2}}-2\sin \theta \cos \theta \\ & y=1-2\sin \theta \cos \theta \\ & y=1-\sin 2\theta \text{ }\left| note:\sin 2\theta =2\sin \theta \cos \theta \right. \\ & \frac{dy}{d\theta }=-2\cos 2\theta \\\end{align}$
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