Problem:
cot10+tan5=
Answer Choices:
A. csc 5
B. csc10
C. sec5
D. sec10
E. sin15
Solution:
Use the definitions of the tangent and cotangent functions and the identity for the cosine of the difference of two angles to obtain
cot10+tan5=sin10cos10+cos5sin5=sin10cos5cos10cos5+sin10sin5=sin10cos5cos(10−5)=sin101=csc10
Note. This is an instance of the identity cot2x+tanx=csc2x.