Question

prove that tan 20°+tan 70°=2 consecutive 40°​

Answer 1

Step-by-step explanation:

$\tan(20) + \tan(70) \\ \frac{ \sin(20) }{ \cos(20) } + \frac{ \sin(70) }{ \cos(70) } \\ \frac{ \sin(20) \times \cos(70) + \cos(20) \times \sin(70) }{ \cos(20) \times \cos(70) } \\ \frac{ \sin(90) }{ \cos(20) \times \sin(90 - 70) } \\ \frac{1}{ \sin(20) \times \cos(20) } \\ \frac{2}{2( \sin(20) \times \cos(20)) } \\ \frac{2}{ \sin(2 \times 20) } \\ \frac{2}{ \sin(40) } \\ 2 \cosec(40)$