सिध्द कीजिए कि : `tan 70^(@) - tan 20^(@) -2 tan 40^(@) =4 tan 10^(@)`

Explanation

`tan 70^(@) - tan 20^(@) -2 tan 40^(@)`
` = [(sin 70^(@))/(cos 70^(@)) -(sin 20^(@))/(cos 20^(@))]- 2 tan 40^(@)`
` =[(sin 70^(@) cos 20^(@) - cos 70^(@) sin 20^(@))/(cos 70^(@) cos 20^(@))] - 2 tan 40^(@)`
` = (sin (70^(@) -20^(@)))/(cos 70^(@) cos 20^(@)) -2 tan 40^(@)`
` = (2 sin 50^(@))/(2 cos 70^(@) cos 20^(@)) -2 tan 40^(@)`
`[ :' 2 cos A cos B = cos (A+ B) + cos (A- B)]`
`= (2 sin 50^(@))/(cos 90^(@) + cos 50^(@))- 2 tan 40^(@)`
`= 2 tan 50^(@) - 2tan 40^(@)`
`=2 [(sin 50^(@) )/(cos 50^(@)) - (sin 40^(@))/(cos 40^(@)) ]`
`=2 [(sin 50^(@) cos 40^(@) -cos 50^(@) sin 40^(@))/(cos 50^(@) cos 40^(@))]`
`= 2 [ (sin (50^(@) -40^(@)))/(cos 50^(@) cos 40^(@))] = (4 sin 10^(@))/(2 cos 50^(@) cos 40^(@))`
`= (4 sin 10^(@))/(cos 90^(@) + cos 10^(@)) = (4 sin 10^(@))/(cos 10^(@))`
`= 4 tan 10^(@)`
`=`दायाँ पक्ष ।