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Trigonometrical Equations
medium
If $\cos A\sin \left( {A - \frac{\pi }{6}} \right)$ is maximum, then the value of $A$ is equal to
A
$\frac{\pi }{3}$
B
$\frac{\pi }{4}$
C
$\frac{\pi }{2}$
D
None of these
Solution
(a) $\cos A\sin \left( {A – \frac{\pi }{6}} \right) = \frac{1}{2}\,\left[ {\sin \left( {2A – \frac{\pi }{6}} \right) – \sin \frac{\pi }{6}} \right]$
But $\sin \left( {2A – \frac{\pi }{6}} \right) – \frac{1}{2}$
attain maximum value at $2A – \frac{\pi }{6} = \frac{\pi }{2} \Rightarrow A = \frac{\pi }{3}$.
Standard 11
Mathematics
