Question

Determine o valor de log (cos0) + $2^{3.cos (0,5 \pi )$ - cos $\frac{2 \pi }{3}$

Answer 1

Olá, Sara.


$\log \cos 0+2^{3\cos0,5 \pi }-\cos \frac{2 \pi }{3} =\log1+2^{3\cos\frac \pi 2}-(\cos^2\frac\pi 3-\sin^2\frac\pi 3)=\\\\=0+2^{3\cdot0}-[(\frac12)^2-(\frac{\sqrt3}2)^2]=1-[\frac14-\frac34]=1-(-\frac24)=1+\frac12=\frac32$