SOLUTION: {{{"tan15°"/"cot75°"}}} + {{{"sin35°"/"cos55°"}}}

15° and 75° are complementary angles, because their sum 15°+75° is 90°
Tangent and cotangent are complementary functions, usually called "cofunctions".
Complementary functions of complementary angles are equal.

Therefore  tan15° = cot75°  therefore  = 1

Similarly 35° and 55° are complementary angles, because their sum 35°+55° is 90°,
Sine and cosine are complementary functions, or "cofunctions". As above,
complementary functions of complementary angles are equal.

Therefore  sin35° = cos55°  therefore  = 1

So,  +  = 1 + 1 = 2.

Edwin