Question 1169459

{{{cos(2tan^-1(2/1))}}}

Use the following identity :

{{{cos(2x)= (-1+2 cos ^2(x))}}}

since {{{x=tan^-1(2/1)=tan^-1(2)}}}, we have

{{{cos(2tan^-1(2))= (-1+2cos ^2(tan^-1(2)))}}}

Use the following identity: {{{cos(tan^-1(x))=(sqrt(1+x^2)/(1+x^2))}}}

{{{cos(2tan^-1(2/1))= (-1+2(sqrt(1+x^2)/(1+x^2))^2)}}}

{{{cos(2tan^-1(2/1))= (-1+2(sqrt(1+2^2)/(1+2^2))^2)}}}

{{{cos(2tan^-1(2/1))= -1+2((1+4)/(1+4)^2)}}}
 
{{{cos(2tan^-1(2/1))= -1+2(5/25)}}}
 
{{{cos(2tan^-1(2/1))= -1+2/5 }}}

{{{cos(2tan^-1(2/1))= -3/5 }}}

{{{cos(2tan^-1(2/1))= -0.6 }}}