[tex]sin210^{o} =sin(180^{o} +30^{o} )=-sin30^{o} =-\dfrac{1}{2} \\\\cos240^{o} =cos(180^{o} +60^{o} )=-cos60^{o}=-\dfrac{1}{2}\\\\tg135^{o} =tg(90^{o} +45^{o} )=-ctg45^{o} =-1\\\\ctg315^{o} =ctg(360^{o} -45^{o} )=-ctg45^{o} =-1\\\\\\\\(sin210^{o}+cos240^{o})\cdot (\dfrac{tg135^{o} }{ctg315^{o} } )=(-\dfrac{1}{2}-\dfrac{1}{2})\cdot (\dfrac{-1}{-1} )=-1\cdot 1 = -1\\\\\\korzystam ~~ze~~wzorow:\\\\sin(180^{o} +\alpha )=-sin\alpha \\\\cos(180^{o} +\alpha )=-cos\alpha \\[/tex]
[tex]tg(90^{o} +\alpha )=-ctg\alpha \\\\ctg(360^{o} +\alpha )=-ctg\alpha[/tex]
dodatkowe wyjaśnienia:
sin210°=sin(270°-60°)=-cos60°= - 1/2
cos240°=cos(270°-30°)=-sin30°= - 1/2
