Qual o valor da expressão (sen pi/8 - cos pi/8)² ?
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Boa noite!
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![\left[\sin\left(\dfrac{\pi}{8}\right)-\cos\left(\dfrac{\pi}{8}\right)\right]^2\\\sin^2\left(\dfrac{\pi}{8}\right)-2\sin\left(\dfrac{\pi}{8}\right)\cos\left(\dfrac{\pi}{8}\right)+\cos^2\left(\dfrac{\pi}{8}\right)\\\overbrace{\sin^2\left(\dfrac{\pi}{8}\right)+\cos^2\left(\dfrac{\pi}{8}\right)}^1-\overbrace{2\sin\left(\dfrac{\pi}{8}\right)\cos\left(\dfrac{\pi}{8}\right)}^{\sin\left(2\dfrac{\pi}{8}\right)}\\1-\sin\left(\dfrac{\pi}{4}\right)\\1-\dfrac{\sqrt{2}}{2}\\\boxed{\dfrac{2-\sqrt{2}}{2}}](https://tex.z-dn.net/?f=%5Cleft%5B%5Csin%5Cleft%28%5Cdfrac%7B%5Cpi%7D%7B8%7D%5Cright%29-%5Ccos%5Cleft%28%5Cdfrac%7B%5Cpi%7D%7B8%7D%5Cright%29%5Cright%5D%5E2%5C%5C%5Csin%5E2%5Cleft%28%5Cdfrac%7B%5Cpi%7D%7B8%7D%5Cright%29-2%5Csin%5Cleft%28%5Cdfrac%7B%5Cpi%7D%7B8%7D%5Cright%29%5Ccos%5Cleft%28%5Cdfrac%7B%5Cpi%7D%7B8%7D%5Cright%29%2B%5Ccos%5E2%5Cleft%28%5Cdfrac%7B%5Cpi%7D%7B8%7D%5Cright%29%5C%5C%5Coverbrace%7B%5Csin%5E2%5Cleft%28%5Cdfrac%7B%5Cpi%7D%7B8%7D%5Cright%29%2B%5Ccos%5E2%5Cleft%28%5Cdfrac%7B%5Cpi%7D%7B8%7D%5Cright%29%7D%5E1-%5Coverbrace%7B2%5Csin%5Cleft%28%5Cdfrac%7B%5Cpi%7D%7B8%7D%5Cright%29%5Ccos%5Cleft%28%5Cdfrac%7B%5Cpi%7D%7B8%7D%5Cright%29%7D%5E%7B%5Csin%5Cleft%282%5Cdfrac%7B%5Cpi%7D%7B8%7D%5Cright%29%7D%5C%5C1-%5Csin%5Cleft%28%5Cdfrac%7B%5Cpi%7D%7B4%7D%5Cright%29%5C%5C1-%5Cdfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%5C%5C%5Cboxed%7B%5Cdfrac%7B2-%5Csqrt%7B2%7D%7D%7B2%7D%7D "\left[\sin\left(\dfrac{\pi}{8}\right)-\cos\left(\dfrac{\pi}{8}\right)\right]^2\\\sin^2\left(\dfrac{\pi}{8}\right)-2\sin\left(\dfrac{\pi}{8}\right)\cos\left(\dfrac{\pi}{8}\right)+\cos^2\left(\dfrac{\pi}{8}\right)\\\overbrace{\sin^2\left(\dfrac{\pi}{8}\right)+\cos^2\left(\dfrac{\pi}{8}\right)}^1-\overbrace{2\sin\left(\dfrac{\pi}{8}\right)\cos\left(\dfrac{\pi}{8}\right)}^{\sin\left(2\dfrac{\pi}{8}\right)}\\1-\sin\left(\dfrac{\pi}{4}\right)\\1-\dfrac{\sqrt{2}}{2}\\\boxed{\dfrac{2-\sqrt{2}}{2}}")
Espero ter ajudado!
Desenvolvendo:
Espero ter ajudado!
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