Question

tan20/tan70+tan40/tan50​

Answer 1

Step-by-step explanation:

$\frac{ \tan(20) }{ \tan(70) } + \frac{ \tan(40) }{ \tan(50) } \\ = \frac{ \tan(90 - 70) }{ \tan(70) } + \frac{ \tan(90 - 50) }{ \tan(50) } \\ = \frac{ \cot(70) }{ \tan(70) } + \frac{ \cot(50) }{ \tan(50) } \\ = \frac{ \frac{1}{ \tan(70) } }{ \tan(70) } + \frac{ \frac{1}{ \tan(50) } }{ \tan(50) } \\ = \frac{1}{ \tan(70) . \tan(70) } + \frac{1}{ \tan(50) . \tan(50) } \\ = \frac{1}{ { \tan}^{2} (70)} + \frac{1}{ { \tan}^{2}(50) } \\ = \frac{ {tan}^{2}(50) + { \tan}^{2}(70) }{ {tan}^{2}(70). {tan}^{2}(50) }$