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.  The answer can be one of the following.

$3\frac{ Tan\ 67}{Cot\ 23}+\frac{1}{\frac{2\ Sin\ 42}{Cos\ 48}}+\frac{5}{\frac{2\ Cosec\ 61}{Sec\ 29}}\\\\=3\frac{tan\ 67}{Cot(90-67)}+\frac{1}{2}\frac{Cos48}{Sin42}+\frac{5}{2}\frac{Sec29}{Cosec61}\\\\=3\frac{tan67}{tan67}+\frac{1}{2}\frac{Cos58}{Sin(90-58)}+\frac{5}{2}\frac{sin61}{cos29}=3+\frac{cos58}{cos58}+\frac{5}{2}\frac{sin61}{Cos(90-61)}\\\\=3+1/2+5/2=6$

==================================

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