sin3a/cos2a<0 if 'a' lies in ....pls rply
Is that sin^3a or sin(3a) ?
it is sin(3a)
\[\frac{\sin 3a}{\cos 2a}=\frac{\sin (2a+a)}{\cos 2a}=\frac{\sin 2a \cos a+\cos 2a \sin a}{\cos 2a}\]
options 1)(13∏/48,14∏/48) 2)(14∏/48,18∏/48) 3)(18∏/48,23∏/48) 4)(0,∏/2)
\[\frac{2\sin a \cos a \cos a}{\cos 2a}+\sin a=\frac{2\sin a \cos ^2a}{\cos ^2a-\sin ^2a}+\sin a=\]
\[\frac{2\sin a \cos ^2a+\sin a \cos ^2a-\sin ^3a}{\cos ^2a-\sin^2a}=\frac{3\sin a \cos ^2a-\sin ^3a}{\cos ^2a-\sin ^2a}=\]
\[\frac{\sin a(3\cos ^2a-\sin ^2a)}{(\cos a-\sin a)(\cos a+\sin a)}\]
If you have the answers, it is easier to just try them out.
\[\frac{\sin 3a}{\cos 2a}= \frac{\sin \frac{13\pi}{16}}{\cos \frac{13\pi}{24}}=\frac{+}{-}=-\]
\[\frac{\sin \frac{14\pi}{16}}{\cos \frac{14\pi}{24}}=\frac{+}{-}=-\]
Looks like choice A works.
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