Question

Sendo x=30, calcule o valor da expressão:
y= 2 senx -4 cosx + tg 2x / cos 4x-sen 2x

Answer 1

y= 2 sen 30 - 4 cos 30 + tg 60/ cos 120- sen 60

Sen 30= $\frac{1}{2}$ , cos 30 =$\sqrt{3}/2$, tg 60 = $\sqrt{3}$

logo,

y= 2.$\frac{1}{2}$- 4. $\sqrt{3} /2$ + $\sqrt{3}$ / -$\frac{1}{2}$ - $\sqrt{3} /2$

Logo.
 
Y= 1- $2\sqrt{3}$ + $\sqrt{3}$ / $- \frac{1}{2} - \sqrt{3}/2$

Y = $1- 2\sqrt{3} + \sqrt{3} / -\frac{1}{2} - \sqrt{3}/2$

Y= $1- 2 \sqrt{3} + \sqrt{3}$ x 2 / $- 1 - \sqrt{3}$

Y= $2 - 4 \sqrt{3} + 2 \sqrt{3}$ x 1 / -1/$\sqrt{3}$

Y = $2 - 2 \sqrt{3}$ x 1 / $-1 - \sqrt{3}$
 
y = 2- $2 \sqrt{3}$

pois,

Y = $2 - 2 \sqrt{3}$ x 1 / $-1 - \sqrt{3}$

Y= ( 2-$2 \sqrt{3}$) x ( $-1 - \sqrt{3}$) x1 / $( -1 - \sqrt{3} )$

Y = 2- $2 \sqrt{3}$

 

Answer 2

x = 30º

sen(30º) = 1/2 ; cos(30º) = √3/2 ; tg(60º) = √3

cos(120º) = -1/2 ; sen(60) = √3/2

▓  Fazendo contas:

y= 2 senx -4 cosx + tg 2x / cos 4x-sen 2x

y = [ 2 * (1/2) - 4 * √3/2 + √3 ] / [-1/2 - √3/2]

y = [ 1 - 2√3 + √3 ] / [-2 - √3 ]/2

y = [ 1 - √3] / [-2 - √3]/2

y = [1 - √3] * 2/[-2 - √3]

y = 2[1 - √3] / -[2 + √3]

y =  2[1 - √3] * [2  - √3] / -[2  + √3] * [2  - √3]

y = [10 - 8√3] / -1

y = -10 + 8√3

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19/03/2016
Sepauto - SSRC
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