a) $\frac{1}{2}\leq sin^{4}\measuredangle + cos^{4}\measuredangle \leq 1$
b) $\frac{1}{4}\leq sin^{6}\measuredangle + cos^{6}\measuredangle \leq 1$
Edited by iloveyou123, 28-09-2012 - 20:04.
$\frac{1}{2}\leq sin^{4}\measuredangle +cos^{4}\measuredangle \leq 1$
Started By iloveyou123, 28-09-2012 - 11:29
#1
Posted 28-09-2012 - 11:29
iloveyou123
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cmr $\forall \measuredangle$ ta luôn có
a) $\frac{1}{2}\leq sin^{4}\measuredangle + cos^{4}\measuredangle \leq 1$
b) $\frac{1}{4}\leq sin^{6}\measuredangle + cos^{6}\measuredangle \leq 1$
a) $\frac{1}{2}\leq sin^{4}\measuredangle + cos^{4}\measuredangle \leq 1$
b) $\frac{1}{4}\leq sin^{6}\measuredangle + cos^{6}\measuredangle \leq 1$
#2
Posted 28-09-2012 - 11:37
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Thành viên nổi bật 2015
Ta có: $sin^{4}A\leq sin^{2}A,cos^{4}A\leq cos^{2}A$ suy ra $sin^{4}A+cos^{4}A\leq 1$
Lại có:$2(sin^{4}A+cos^{4}A)\geq \left ( sin^{2}A+cos^{2}A \right )^{2}=1$?
Lại có:$2(sin^{4}A+cos^{4}A)\geq \left ( sin^{2}A+cos^{2}A \right )^{2}=1$?
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