Before we try and evaluate let us go over these identities.
#cos(360n+theta) = cos(theta)#
#cos(-theta) = cos(theta)#
#sin(theta)/cos(theta) = tan(theta)#
#sin(-theta) = -sin(theta)#
#tan(-theta) = -tan(theta)#
Now let us come to our problem
#sin(70^o)/cos(-430^o) + tan(-70^o)#
#=sin(70^o)/cos(430^o)-tan(70^o)# #quad color(red) "since"quad tan(-theta)=tan(theta) and cos(-theta)=cos(theta)#
#=sin(70^o)/cos(360^o +70^o)-tan(70^o)##quad color(red) "since"quad 430=360+70#
#=sin(70^o)/cos(70^o) - tan(70^o) ##quad color(red) "since"quad cos(360+theta)=cos(theta)#
#=tan(70^o)-tan(70^o)# #quad color(red) "since"quad sin(theta)/cos(theta) = tan(theta)#
#=0# Answer
