Question

Vectors a and b include an angle theta between them. If ( a+b) and (a-b) respectively subtend angles alpha and beta with a then ( tan alpha + tan beta ) is

Answer 1

Answer:

tanα + tanβ  = 2absinθ/a²-b²cos²θ

Explanation:

Given that the angle between a and b is θ

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

tanα = bsinθ/(a+bcosθ)

similarly (a-b) makes an angle of β with a, hence

tanβ = bsinθ/(a-bcosθ)

Adding both the equation we get,

tanα + tanβ = bsinθ/(a+bcosθ) + bsinθ/(a-bcosθ)

= bsinθ[ 1/(a+bcosθ) + 1/(a-bcosθ)]

= bsinθ[(a-bcosθ + a+bcosθ)/(a+bcosθ)(a-bcosθ)]

=>tanα + tanβ  = 2absinθ/a²-b²cos²θ

which is the required value.

Answer 2

Answer:

Explanation: 3rd question