Question 873344
sec(x)=radical 5 with sinx>0, find tan(2x)
Given reference angle x is in quadrant I
{{{secx=sqrt(5)}}}
{{{cosx=1/secx=1/sqrt(5)=sqrt(5)/5}}}
{{{sinx=sqrt(1-cos^2(x))=sqrt(1-(5/25))=sqrt(20/25)=sqrt(20)/5)}}}
{{{tanx=sinx/cosx=sqrt(20)/sqrt(5)=sqrt(4)=2}}}
Identity: {{{tan(2x)=(2tanx)/(1-tan^2(x))=4/(1-4)=4/-3=-4/3}}}
Calculator check:
cosx=√5/5
x≈63.43˚
2x≈126.86˚
tan 2x≈tan(126.86)≈-1.333…
exact value as calculated above=-4/3≈-1.333…