cos(346)=cos(346-360)=cos(-14)=cos(14).
cos(14)=sin(90-14)=sin(76), and sin(14)=cos(76).
sin(121)=sin(180-121)=sin(59).
We can reduce the size of all angles greater than 90°:
cos(56)cos(14)+sin(59)sin(14). If cos(56) had been cos(59) then:
cos(59)cos(14)+sin(59)sin(14)=cos(59-14)=cos45=√2/2, because it's an identity.
It seems likely that the question should have been: evaluate cos(59).cos(346)+sin(121).cos(76).
From this example you can see how the trig function can be the same value for different sized angles. The range 0-360 can be divided into quadrants: Q1=0-90, Q2=90-180, Q3=180-270, Q4=270-360. After 360°, we get to Q1 again for the range 360-450, and so on, so all angles can be reduced to angles in Q1. But if q1, q2, q3, q4 are angles in quadrants Q1, Q2, Q3, Q4, their trig values change signs.
In Q1 all trig values are positive; trig values for q2 only sin(q2) is positive; for q3, only tan(q3) is positive; and for q4, only cos(q4) is positive. The mnemonic All-Silver-Tea-Cups (all, sine, tangent, cosine in Q1, Q2, Q3, Q4 respectively) is useful to tell you which trig functions are positive and which are negative. This rule applies also to inverse trig functions cosecant, cotangent, secant.