Question

1. Cho sinx = 4/5 và 90<x<180, tan2x bằng

2. Cho sinx = 1/2 và 0<x<90, cos2x bằng

Answer 1

1: 90<x<180

=>cosx<0

=>\(cosx=-\sqrt{1-\left(\dfrac{4}{5}\right)^2}=-\dfrac{3}{5}\)

\(sin2x=2\cdot sinx\cdot cosx=2\cdot\dfrac{4}{5}\cdot\dfrac{-3}{5}=\dfrac{-24}{25}\)

\(cos2x=2\cdot cos^2x-1=2\cdot\dfrac{9}{25}-1=-\dfrac{7}{25}\)

\(tan2x=\dfrac{-24}{25}:\dfrac{-7}{25}=\dfrac{24}{7}\)

2: 0<x<90

=>cosx>0

=>\(cosx=\sqrt{1-\left(\dfrac{1}{2}\right)^2}=\dfrac{\sqrt{3}}{2}\)

\(cos2x=2\cdot cos^2x-1=2\cdot\dfrac{3}{4}-1=\dfrac{6}{4}-1=\dfrac{2}{4}=\dfrac{1}{2}\)