Question

Simplificar expressão e calcular cosseno

Answer 1

Resposta:

!

Explicação passo-a-passo:

Sen ( a +b) = Sen a.Cos b + Sen b.Cos a

Cos ( a + b) = Cos a.Cos b - Sen a. Sen b

Cos ( a - b) = Cos a. Cos b + Sen a. Sen b

2.

$E = Sen\frac{\pi }{2}+Sen(\frac{\pi }{2}+x) .Cos(3\pi-x)\\E = 1+(Sen\frac{\pi }{2}.Cos x+Senx.Cos\frac{\pi}{2}).(Cos3\pi.Cosx+Sen3\pi.Senx)\\E = 1+(1.Cosx + Senx.0).((-1).Cosx+0.Senx)\\E = 1 +Cosx.(-1.Cosx)\\E = 1 -1.Cos^2x\\\\Sen^2x+Cos^2x=1\\Cos^2x= 1-Sen^2x\\\\E = 1 -1.(1 -Sen^2x)\\E = 1 -1 +Sen^2x\\E = Sen^2x$

3.

$Sena = \frac{1}{2}\\Cos b = \frac{1}{3}\\\\Sen^2x+Cos^2x = 1\\\\(1/2)^2+Cos^2a=1\\Cos^2a= 1-1/4\\Cos^2a = 3/4\\Cos a = \sqrt{3/4}\\Cos a = \sqrt{3}/2\\ \\Sen^2b+(1/3)^2 = 1\\Sen^2b = 1 -1/9\\Sen^2b = 8/9\\Sen b = \sqrt{8/9}\\Sen b = 2\sqrt{2}/3\\ \\Cos ( a +b) = Cos a.Cos b - Sen a. Sen b\\Cos ( a +b) = \sqrt{3}/2.1/3 -1/2.2\sqrt{2}/3\\Cos ( a +b) = \sqrt{3}/6 - 2\sqrt{2}/6 \\Cos ( a +b) = \frac{\sqrt{3}-2\sqrt{2}  }{6}$

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