[tex]sin(180^{o} +\alpha )=sin(\pi +\alpha )=-sin\alpha \\\\sin240^{o} =sin(180^{o} +60^{o} )=-sin60^{o} \\\\sin240^{o} =-sin60^{o} ~~~~\land~~~sin60^{o} =\dfrac{\sqrt{3} }{2} ~~~~\Rightarrow~~sin240^{o} =-\dfrac{\sqrt{3} }{2}\\\\\\ctg(90^{o} +\alpha )=ctg(\dfrac{\pi }{2} +\alpha )=-tg\alpha \\\\ctg135^{o} =ctg(90^{o} +45^{o} )=-tg45^{o} \\\\ctg135^{o} =-tg45^{o}~~~~\land~~~tg45^{o}=1~~~~\Rightarrow~~ctg135^{o} =-1[/tex]
