Question

Si: COSX - senx = 0,5 calcular : sen2x​

Answer 1

Recordar;

$\sin(2x)=2\cos(x).\sin(x)$

$\cos^2x+\sin^2x=1$

Elevando al cuadrado;

$(\cos x-\sin x)^{2} =(\dfrac{1}{2})^2$

$\cos^2x-2.\sin x . \cos x + \sin^2 x =\dfrac{1}{4}$

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

$1-\sin2x=\dfrac{1}{4}$

$\sin2x=1-\dfrac{1}{4}$

$\boxed{\sin2x=\dfrac{3}{4}}$