Question

tan 70-tan 20 =mcot 40 Then m=?

Answer 1

$\tan70 - \tan20 = \cot(90 - 70) - \tan20 \\ = \cot20 - \tan20 = \frac{1}{ \tan20 } - \tan20 \\ = \frac{1 - { \tan}^{2} 20}{ \tan20} = \frac{2}{ \frac{2 \tan20}{1 - { \tan}^{2} 20} } \\ = \frac{2}{ \tan(2 \times 20) } = \frac{2}{ \tan40} = 2 \cot40$
Therefore m = 2