Question

8) Si sen B = 1/2 , calcular y= (cos2B – sen2B)tg2B

Answer 1

Respuesta:

Explicación paso a paso:

sen B = 1/2 = y/h

Teorema de Pitágoras

x² + y² = h²

x² + 1² = 2²

x² = 4-1

x = $\sqrt{3}$

cos B = $\sqrt{3}$/2

cos 2B = cos² B - sen² B = ($\sqrt{3}$/2)² - (1/2)² = 1/2

sen 2B = 2sen B.cos B = 2(1/2)($\sqrt{3}$/2) = $\sqrt{3}$/2

tg 2B = sen 2B/cos 2B = $\sqrt{3}$

calcular y= (cos2B – sen2B)tg2B

y = (1/2 - $\sqrt{3}$/2)($\sqrt{3}$) = ($\sqrt{3}$ - 1)/2