we know that tan x =sin x/ cos x sin x/ cos x=5------> squaring-----> sin² x/cos² x=25 remember that sin² x+cos² x=1-----> cos² x=1-sin² x substitute sin² x/[1-sin² x]=25 sin² x=25-25*sin² x 26*sin² x=25 sin² x=25/26 sin x=5/√26
cos² x=1-(5/√26)²----> 1-(25/26)----> 1/26 cos x=1/√26
