Question

3 tan67⁰÷cot23⁰₊1÷2 sin42⁰÷cos48⁰₊5÷2 cosec61⁰÷sec29⁰

Answer 1

You should use parentheses when writing algebraic expressions.  It is not clear sometimes, which factor is in numerator and which is in denominator.

$3\frac{ Tan\ 67}{Cot\ 23}+\frac{1}{2\ Sin\ 42\ *\ Cos\ 48}+\frac{5}{2\ Cosec\ 61\ *\ Sec\ 29}\\\\=3\frac{ Tan\ 67}{Cot\ (90-67)}+\frac{1}{2\ Sin\ 42\ *\ Cos(90-42)}+\frac{5}{2}Sin\ 61\ *\ Cos\ 29\\\\=3\frac{Tan\ 67}{Tan\ 67}+\frac{1}{2\ Sin^2\ 42}+\frac{5}{2}Sin\ 61*Sin61\\\\=3+3.029=6.029$