Question

If R makes an angle ß with then tan |​

Answer 1

ANSWER

Given that the angle between

a

and

b

is θ

Since (a + b ) makes an angle of α with

, hence

⟹tan α=

(a+bcos θ)

bsin θ

Similarly, ( a − b ) makes an angle of β with a , Hence

⟹tan β=

(a−bcos θ)

bsin θ

Adding both the equation we get,

⟹tan α+tan β=

(a+bcos θ)

bsin θ + (a−bcos θ)bsin θ

⟹tan α+tan β=bsinθ[

(a+bcosθ)

1

+

(a−bcosθ)1 ]

⟹tan α+tan β=bsinθ[

(a+bcosθ)(a−bcosθ)

(a−bcosθ+a+bcosθ)

]

⟹tan α+tan β=

a²−b²cos²θ

2absinθ

$I HOPE ITS HELPFULL ☺️$