Rút gọn các biểu thức sau:
$F=\frac{2cos^2a-1}{2tan(\frac{\pi}{4}-a)sin^2(\frac{\pi}{4}+a)}$
$G=\frac{sin(60^o+a)}{4sin(15^o+\frac{a}{4})sin(75^o-\frac{a}{4})}$
Rút gọn các biểu thức sau:
$F=\frac{2cos^2a-1}{2tan(\frac{\pi}{4}-a)sin^2(\frac{\pi}{4}+a)}$
$G=\frac{sin(60^o+a)}{4sin(15^o+\frac{a}{4})sin(75^o-\frac{a}{4})}$
Rút gọn các biểu thức sau:
$F=\frac{2cos^2a-1}{2tan(\frac{\pi}{4}-a)sin^2(\frac{\pi}{4}+a)}$
$G=\frac{sin(60^o+a)}{4sin(15^o+\frac{a}{4})sin(75^o-\frac{a}{4})}$
$F=\frac{2\cos^2a-1}{2\tan(\frac{\pi}{4}-a)\sin^2(\frac{\pi}{4}+a)}$
$=\frac{\cos2a\cos\left ( \frac{\pi}{4}-a \right ) }{\left (2\sin(\frac{\pi}{4}-a)\sin(\frac{\pi}{4}+a) \right )\sin(\frac{\pi}{4}+a)}$
$=\frac{\cos2a\cos\left ( \frac{\pi}{4}-a \right )}{\left ( \cos2a-\cos\frac{\pi}{2} \right )\sin(\frac{\pi}{4}+a)}$
$=\frac{\cos\left ( \frac{\pi}{4}-a \right )\cos\left ( \frac{\pi}{4}+a \right )}{\sin(\frac{\pi}{4}+a)\cos\left ( \frac{\pi}{4}+a \right )}$
$=\frac{\cos\frac{\pi}{2}+\cos2a}{\cos2a}=1$
$G=\frac{\sin(60^0+a)}{4\sin(15^0+\frac{a}{4})\sin(75^0-\frac{a}{4})}$
$=\frac{\sin(60^0+a)}{2\left [ \cos\left ( 60^0-\frac{a}{2} \right )-\cos90^0 \right ]}$
$=\frac{\sin(120^0-a)}{2\cos\left ( 60^0-\frac{a}{2} \right )}$
$=\frac{2\sin\left ( 60^0-\frac{a}{2} \right )\cos\left ( 60^0-\frac{a}{2} \right )}{2\cos\left ( 60^0-\frac{a}{2} \right )}$
$=\sin\left ( 60^0-\frac{a}{2} \right )$
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