To find tg(x+y), we can use the relation:
tg(x+y) = (tgx + tgy) / (1 - tgxtgy)
Given that Tgx + Tgy = 4 and cosx * cosy = 1/5, we can find tgx and tgy using the trigonometric identity:
tgx = sinx / cosxtgy = sing / cosy
We are also given that cosx × cosy = 1/5. Since cosx * cosy = (cos(x)cos(y) - sin(x)sin(y)), we have:
cosx * cosy = (cos(x)cos(y) - sin(x)sin(y)) = 1/5
Given that cos(x)cos(y) = 1/5:3cos(x)cos(y)=4/5 and, sin(x)sin(y)=4√6/5
Therefore, tg(x+y) = (4 + 4√6/5) / (1 - 4/5 × 4√6/5)= (4 + 4√6/5) / (1 - 16√6/25)= [25(4 + 4√6)] / [25 - 16√6]= (100 + 100√6) / (25 - 16√6)
To find tg(x+y), we can use the relation:
tg(x+y) = (tgx + tgy) / (1 - tgxtgy)
Given that Tgx + Tgy = 4 and cosx * cosy = 1/5, we can find tgx and tgy using the trigonometric identity:
tgx = sinx / cosx
tgy = sing / cosy
We are also given that cosx × cosy = 1/5. Since cosx * cosy = (cos(x)cos(y) - sin(x)sin(y)), we have:
cosx * cosy = (cos(x)cos(y) - sin(x)sin(y)) = 1/5
Given that cos(x)cos(y) = 1/5:
3cos(x)cos(y)=4/5 and, sin(x)sin(y)=4√6/5
Therefore, tg(x+y) = (4 + 4√6/5) / (1 - 4/5 × 4√6/5)
= (4 + 4√6/5) / (1 - 16√6/25)
= [25(4 + 4√6)] / [25 - 16√6]
= (100 + 100√6) / (25 - 16√6)