Question

x aparține lui R
$\sin(x) = \frac{1}{2} + \cos(x)$
să se calculeze sin(2x)



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Answer 1

Răspuns:

$sin(x)=\frac{1}{2}+cos(x)=>sin(x)-cos(x)=\frac{1}{2} |*()^2$

$sin^2(x)+cos^2(x)-2sin(x)*cos(x)=\frac{1}{4}$

$1-2sin(x)*cos(x)=\frac{1}{4}$

$-2sin(x)*cos(x)=\frac{1}{4}-1$

$-2sin(x)*cos(x)=-\frac{3}{4}|*(-1)$

$2sin(x)*cos(x)=\frac{3}{4}$

$sin(2x)=\frac{3}{4}$