Question

If α, β, γ ∈ [0, π] and α, β, γ are in AP, then `(sin α - sin γ)/(cos γ - cos α)` is equal to ______.

Options

• sin β

• cos β

• cot β

• cosec β

Answer 1

If α, β, γ ∈ [0, π] and α, β, γ are in AP, then `(sin α - sin γ)/(cos γ - cos α)` is equal to cot β.

Explanation:

Since, α, β, and γ are in AP.

∴ 2β = α + γ

Now, `(sin α - sin γ)/(cos γ - cos α)`

= `(2 cos ((α + γ)/2) sin((α - γ)/2))/(2 sin((α + γ)/2) sin((a - γ)/2))`

= `cot ((a + γ)/2)`

= `cot  ((2β)/2)`  ...[∵ 2β = α + γ]

= cot β